Klausberger, T, Somogyi, P. Neuronal diversity and temporal dynamics: the unity of hippocampal circuit operations. Science 2008, 321:53–57.

Bartol, Jr TM, Bromer, C, Kinney, J, Chirillo, MA, Bourne, JN, Harris, KM, Sejnowski, TJ. Nanoconnectomic upper bound on the variability of synaptic plasticity. eLife 2015, 4. doi:10.7554/eLife.10778.

Coyle, JT. NMDA receptor and schizophrenia: a brief history. Schizophr Bull 2012, 38:920–926.

Walczak, A, Szczepankiewicz, AA, Ruszczycki, B, Magalska, A, Zamlynska, K, Dzwonek, J, Wilczek, E, Zybura‐Broda, K, Rylski, M, Malinowska, M, et al. Novel higher‐order epigenetic regulation of the Bdnf gene upon seizures. J Neurosci 2013, 33:2507–2511.

Hawrylycz, MJ, Lein, ES, Guillozet‐Bongaarts, AL, Shen, EH, Ng, L, Miller, JA, van de Lagemaat, LN, Smith, KA, Ebbert, A, Riley, ZL, et al. An anatomically comprehensive atlas of the adult human brain transcriptome. Nature 2012, 489:391–399.

Robinson, GE. Brains work via their genes just as much as their neurons. Conversation October 14, 2015. https://theconversation.com/brains‐work‐via‐their‐genes‐just‐as‐much‐as‐their‐neurons‐47522.

Fornito, A, Zalesky, A, Breakspear, M. The connectomics of brain disorders. Nat Rev Neurosci 2015, 16:159–172.

Koch, C, Laurent, G. Complexity and the nervous system. Science 1999, 284:96–98.

Destexhe, A, Contreras, D. Neuronal computations with stochastic network states. Science 2006, 314:85–90.

Stam, CJ. Nonlinear dynamical analysis of EEG and MEG: review of an emerging field. Clin Neurophysiol Off J Int Fed Clin Neurophysiol 2005, 116:2266–2301.

Gerstner, W, Sprekeler, H, Deco, G. Theory and simulation in neuroscience. Science 2012, 338:60–65.

van Ooyen, A. Using theoretical models to analyse neural development. Nat Rev Neurosci 2011, 12:311–326.

Xia, M, Wang, J, He, Y. BrainNet Viewer: a network visualization tool for human brain connectomics. PLoS One 2013, 8:e68910.

Abbott, LF. Lapicque`s introduction of the integrate‐and‐fire model neuron (1907). Brain Res Bull 1999, 50:303–304.

McCulloch, WS, Pitts, W. A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys 1943, 5:115–133.

Hodgkin, AL, Huxley, AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 1952, 117:500–544.

Rall, W. Electrophysiology of a dendritic neuron model. Biophys J 1962, 2:145–167.

FitzHugh, R. Mathematical models of threshold phenomena in the nerve membrane. Bull Math Biophys 1955, 17:257–278.

Nagumo, J, Arimoto, S, Yoshizawa, S. An active pulse transmission line simulating nerve axon. Proc IRE 1962, 50:2061–2070.

Wiener, N, Rosenblueth, A. The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle. Arch Inst Cardiol Mex 1946, 16:205–265.

Greenberg, J, Hastings, S. Spatial patterns for discrete models of diffusion in excitable media. SIAM J Appl Math 1978, 34:515–523.

Smith, DR, Davidson, CH. Maintained activity in neural nets. J ACM 1962, 9:268–279.

Anninos, PA, Beek, B, Csermely, TJ, Harth, EM, Pertile, G. Dynamics of neural structures. J Theor Biol 1970, 26:121–148.

Wilson, HR, Cowan, JD. Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 1972, 12:1–24.

Lorenz, EN. Deterministic nonperiodic flow. J Atmos Sci 1963, 20:130–141.

Lorenz, EN. Atmospheric predictability as revealed by naturally occurring analogues. J Atmos Sci 1969, 26:636–646.

Rössler, OE. An equation for continuous chaos. Phys Lett A 1976, 57:397–398.

Rössler, OE. An equation for hyperchaos. Phys Lett A 1979, 71:155–157.

Hindmarsh, JL, Rose, RM. A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B Biol Sci 1984, 221:87–102.

Korn, H, Faure, P. Is there chaos in the brain? II. Experimental evidence and related models. C R Biol 2003, 326:787–840.

Izhikevich, EM. Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 2004, 15:1063–1070.

Herz, AVM, Gollisch, T, Machens, CK, et al. Modeling single‐neuron dynamics and computations: a balance of detail and abstraction. Science 2006, 314:80–85.

Deco, G, Jirsa, VK, Robinson, PA, Breakspear, M, Friston, K, et al. The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Comput Biol 2008, 4:e1000092.

Jirsa, VK. Connectivity and dynamics of neural information processing. Neuroinformatics 2004, 2:183–204.

Hebb, DO. The Organization of Behavior: A Neuropsychological Theory. New ed. Mahwah, NJ: Psychology Press; 2002.

Granger, CWJ. Investigating causal relations by econometric models and cross‐spectral methods. Econometrica 1969, 37:424–438.

Hockett, CF. Review of the mathematical theory of communication. Language 1953, 29:69–93.

Borst, A, Theunissen, FE. Information theory and neural coding. Nat Neurosci 1999, 2:947–957.

Schreiber, T. Measuring information transfer. Phys Rev Lett 2000, 85:461–464.

Janjarasjitt, S, Loparo, KA. An approach for characterizing coupling in dynamical systems. Phys Nonlinear Phenom 2008, 237:2482–2486.

Vlachos, I, Kugiumtzis, D. Nonuniform state‐space reconstruction and coupling detection. Phys Rev E 2010, 82:016207.

Rabinovich, MI, Varona, P, Selverston, AI, Abarbanel, HDI. Dynamical principles in neuroscience. Rev Mod Phys 2006, 78:1213–1265.

Izhikevich, EM. Dynamical Systems in Neuroscience. Cambridge, MA: MIT Press; 2007.

Marr, D. A theory for cerebral neocortex. Proc R Soc Lond B Biol Sci 1970, 176:161–234.

Grossberg, S. Towards a unified theory of neocortex: laminar cortical circuits for vision and cognition. Prog Brain Res 2007, 165:79–104.

Wilson, HR, Cowan, JD. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 1973, 13:55–80.

Elijah, DH, Samengo, I, Montemurro, MA. Thalamic neuron models encode stimulus information by burst‐size modulation. Front Comput Neurosci 2015, 9:113.

Safaai, H, Neves, R, Eschenko, O, Logothetis, NK, Panzeri, S. Modeling the effect of locus coeruleus firing on cortical state dynamics and single‐trial sensory processing. Proc Natl Acad Sci USA 2015, 112:12834–12839.

Traub, RD, Wong, RK, Miles, R, et al. A model of a CA3 hippocampal pyramidal neuron incorporating voltage‐clamp data on intrinsic conductances. J Neurophysiol 1991, 66:635–650.

Yamaguti, Y, Kuroda, S, Fukushima, Y, et al. A mathematical model for Cantor coding in the hippocampus. Neural Netw Off J Int Neural Netw Soc 2011, 24:43–53.

Ermentrout, GB, Cowan, JD. A mathematical theory of visual hallucination patterns. Biol Cybern 1979, 34:137–150.

Bressloff, PC, Cowan, JD, Golubitsky, M, Thomas, PJ, Wiener, MC. What geometric visual hallucinations tell us about the visual cortex. Neural Comput 2002, 14:473–491.

Haken, H, Kelso, JAS, Bunz, H. A theoretical model of phase transitions in human hand movements. Biol Cybern 1985, 51:347–356.

Kelso, JAS. Instabilities and phase transitions in human brain and behavior. Front Hum Neurosci 2010, 4. doi:10.3389/fnhum.2010.00023.

Jirsa, VK, Friedrich, R, Haken, H, Kelso, JA. A theoretical model of phase transitions in the human brain. Biol Cybern 1994, 71:27–35.

Durstewitz, D, Seamans, JK, Sejnowski, TJ. Neurocomputational models of working memory. Nat Neurosci 2000, 3:1184–1191.

Laing, CR, Troy, WC, Gutkin, B, Ermentrout, GB. Multiple bumps in a neuronal model of working memory. SIAM J Appl Math 2002, 63:62–97.

Durstewitz, D, Seamans, JK. Beyond bistability: biophysics and temporal dynamics of working memory. Neuroscience 2006, 139:119–133.

Cohen, JD, Braver, TS, O`Reilly, RC. A computational approach to prefrontal cortex, cognitive control and schizophrenia: recent developments and current challenges. Philos Trans R Soc Lond B Biol Sci 1996, 351:1515–1527.

Hoffman, RE, McGlashan, TH. Synaptic elimination, neurodevelopment, and the mechanism of hallucinated “voices” in schizophrenia. Am J Psychiatry 1997, 154:1683–1689.

Rolls, ET, Deco, G. A computational neuroscience approach to schizophrenia and its onset. Neurosci Biobehav Rev 2011, 35:1644–1653.

Babloyantz, A, Destexhe, A. Low‐dimensional chaos in an instance of epilepsy. Proc Natl Acad Sci 1986, 83:3513–3517.

Netoff, TI, Clewley, R, Arno, S, Keck, T, White, JA. Epilepsy in small‐world networks. J Neurosci 2004, 24:8075–8083.

Rubin, JE, Terman, D. High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model. J Comput Neurosci 2004, 16:211–235.

Strogatz, SH. Exploring complex networks. Nature 2001, 410:268–276.

Morris, C, Lecar, H. Voltage oscillations in the barnacle giant muscle fiber. Biophys J 1981, 35:193–213.

Izhikevich, EM. Simple model of spiking neurons. Trans Neur Netw 2003, 14:1569–1572.

Boerlin, M, Machens, CK, Denève, S. Predictive coding of dynamical variables in balanced spiking networks. PLoS Comput Biol 2013, 9:e1003258.

Saparov, A, Schwemmer, MA. Effects of passive dendritic tree properties on the firing dynamics of a leaky‐integrate‐and‐fire neuron. Math Biosci 2015, 269:61–75.

Torres, JJ, Marro, J. Brain performance versus phase transitions. Sci Rep 2015, 5:12216.

Lago‐Fernández, LF, Huerta, R, Corbacho, F, Sigüenza, JA. Fast response and temporal coherent oscillations in small‐world networks. Phys Rev Lett 2000, 84:2758–2761.

Terman, D, Ahn, S, Wang, X, Just, W. Reducing neuronal networks to discrete dynamics. Phys Nonlinear Phenom 2008, 237:324–338.

Ashwin, P, Coombes, S, Nicks, R. Mathematical frameworks for oscillatory network dynamics in neuroscience. J Math Neurosci 2016, 6:2.

Fine, AS, Nicholls, DP, Mogul, DJ. Assessing instantaneous synchrony of nonlinear nonstationary oscillators in the brain. J Neurosci Methods 2010, 186:42–51.

Hadjipapas, A, Casagrande, E, Nevado, A, Barnes, GR, Green, G, Holliday, IE. Can we observe collective neuronal activity from macroscopic aggregate signals? Neuroimage 2009, 44:1290–1303.

Barrio, R, Shilnikov, A. Parameter‐sweeping techniques for temporal dynamics of neuronal systems: case study of Hindmarsh‐Rose model. J Math Neurosci 2011, 1:6.

Lainscsek, C, Weyhenmeyer, J, Hernandez, ME, Poizner, H, Sejnowski, TJ. Non‐linear dynamical classification of short time series of the Rössler system in high noise regimes. Front Neurol 2013, 4. doi:10.3389/fneur.2013.00182.

Selverston, AI, Rabinovich, MI, Abarbanel, HD, Elson, R, Szücs, A, Pinto, RD, Huerta, R, Varona, P. Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators. J Physiol Paris 2000, 94:357–374.

Sungar, N, Allaria, E, Leyva, I, Arecchi, FT. Comparison of single neuron models in terms of synchronization propensity. Chaos Woodbury N 2008, 18:033108.

Treves, A. Mean‐field analysis of neuronal spike dynamics. Netw Comput Neural Syst 1993, 4:259–284.

Bressloff, PC, Coombes, S, de Souza, B. Dynamics of a ring of pulse‐coupled oscillators: group‐theoretic approach. Phys Rev Lett 1997, 79:2791–2794.

Haskell, E, Nykamp, DQ, Tranchina, D. Population density methods for large‐scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size. Netw Bristol Engl 2001, 12:141–174.

Casti, ARR, Omurtag, A, Sornborger, A, Kaplan, E, Knight, B, Victor, J, Sirovich, L. A population study of integrate‐and‐fire‐or‐burst neurons. Neural Comput 2002, 14:957–986.

Cai, D, Tao, L, Shelley, M, McLaughlin, DW. An effective kinetic representation of fluctuation‐driven neuronal networks with application to simple and complex cells in visual cortex. Proc Natl Acad Sci USA 2004, 101:7757–7762.

Sanz‐Leon, P, Knock, SA, Spiegler, A, Jirsa, VK. Mathematical framework for large‐scale brain network modeling in The Virtual Brain. Neuroimage 2015, 111:385–430.

Cabral, J, Hugues, E, Sporns, O, Deco, G. Role of local network oscillations in resting‐state functional connectivity. Neuroimage 2011, 57:130–139.

Váša, F, Shanahan, M, Hellyer, PJ, Scott, G, Cabral, J, Leech, R. Effects of lesions on synchrony and metastability in cortical networks. Neuroimage 2015, 118:456–467.

Acebrón, JA, Bonilla, LL, Pérez Vicente, CJ, Ritort, F, Spigler, R. The Kuramoto model: a simple paradigm for synchronization phenomena. Rev Mod Phys 2005, 77:137–185.

Kuramoto, Y. Collective synchronization of pulse‐coupled oscillators and excitable units. Phys Nonlinear Phenom 1991, 50:15–30.

Kuramoto, Y, Nishikawa, I. Statistical macrodynamics of large dynamical systems. Case of a phase transition in oscillator communities. J Stat Phys 1987, 49:569–605.

Strogatz, SH. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators. Phys Nonlinear Phenom 2000, 143:1–20.

Wilson, HR. Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience. Oxford and New York: Oxford University Press; 1999.

Negahbani, E, Steyn‐Ross, DA, Steyn‐Ross, ML, Wilson, MT, Sleigh, JW. Noise‐induced precursors of state transitions in the stochastic Wilson‐Cowan model. J Math Neurosci 2015, 5:1–27.

Kilpatrick, ZP. %22Wilson‐Cowan model%22. In: Jaeger, D, Jung, R, eds. Encyclopedia of Computational Neuroscience. New York: Springer; 2014.

Ermentrout, GB. Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators. SIAM J Appl Math 1992, 52:1665–1687.

Abbott, LF, van Vreeswijk, C. Asynchronous states in networks of pulse‐coupled oscillators. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Top 1993, 48:1483–1490.

Gutkin, BS, Laing, CR, Colby, CL, Chow, CC, Ermentrout, GB. Turning on and off with excitation: the role of spike‐timing asynchrony and synchrony in sustained neural activity. J Comput Neurosci 2001, 11:121–134.

Laing, CR, Chow, CC. A spiking neuron model for binocular rivalry. J Comput Neurosci 2002, 12:39–53.

Coombes, S, Osbaldestin, AH. Period‐adding bifurcations and chaos in a periodically stimulated excitable neural relaxation oscillator. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Top 2000, 62:4057–4066.

Usher, M, Schuster, HG, Niebur, E. Dynamics of populations of integrate‐and‐fire neurons, partial synchronization and memory. Neural Comput 1993, 5:570–586.

Brunel, N, Hakim, V. Fast global oscillations in networks of integrate‐and‐fire neurons with low firing rates. Neural Comput 1999, 11:1621–1671.

Bressloff, PC, Coombes, S. Travelling waves in chains of pulse‐coupled integrate‐and‐fire oscillators with distributed delays. Phys Nonlinear Phenom 1999, 130:232–254.

Omurtag, A, Knight, BW, Sirovich, L. On the simulation of large populations of neurons. J Comput Neurosci 2000, 8:51–63.

Ermentrout, GB, Chow, CC. Modeling neural oscillations. Physiol Behav 2002, 77:629–633.

Wolfram, S. Universality and complexity in cellular automata. Phys Nonlinear Phenom 1984, 10:1–35.

Kozma, R, Puljic, M, Balister, P, Bollobás, B, Freeman, WJ. Phase transitions in the neuropercolation model of neural populations with mixed local and non‐local interactions. Biol Cybern 2005, 92:367–379.

Furtado, LS, Copelli, M. Response of electrically coupled spiking neurons: a cellular automaton approach. Phys Rev E 2006, 73:011907.

Deco, G, Jirsa, VK, Robinson, PA, Breakspear, M, Friston, K. The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Comput Biol 2008, 4:e1000092.

Borisyuk, GN, Borisyuk, RM, Kazanovich, YB, Ivanitskiib, GR. Models of neural dynamics in brain information processing — the developments of “the decade”. Phys‐Uspekhi 2002, 45:1073–1095.

Doedel, EJ, Govaerts, W, Kuznetsov, YA, Dhooge, A. Numerical continuation of branch points of equilibria and periodic orbits. Int J Bifurc Chaos 2005, 15:841–860.

Dhooge, A, Govaerts, W, Kuznetsov, YA. MATCONT: a MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans Math Softw 2003, 29:141–164.

Dankowicz, H, Schilder, F. Recipes for Continuation. Philadelphia, USA: SIAM Bookst; 2013.

Rinzel, J, Ermentrout, GB. %22Analysis of neural excitability and oscillations%22. In: Koch, C, Segev, I, eds. Methods in Neuronal Modeling. Cambridge, MA, USA: MIT Press; 1989, 135–169.

Rinzel, J, Lee, YS. Dissection of a model for neuronal parabolic bursting. J Math Biol 1987, 25:653–675.

Reidl, J, Borowski, P, Sensse, A, Starke, J, Zapotocky, M, Eiswirth, M. Model of calcium oscillations due to negative feedback in olfactory cilia. Biophys J 2006, 90:1147–1155.

Nowotny, T, Rabinovich, MI. Dynamical origin of independent spiking and bursting activity in neural microcircuits. Phys Rev Lett 2007, 98:128106.

Ly, C, Tranchina, D. Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling. Neural Comput 2007, 19:2032–2092.

Theodoropoulos, C, Qian, Y‐H, Kevrekidis, IG. “Coarse” stability and bifurcation analysis using time‐steppers: a reaction–diffusion example. Proc Natl Acad Sci USA 2000, 97:9840–9843.

Kevrekidis, IG, Gear, CW, Hyman, JM, Kevrekidis, PG, Runborg, O, Theodoropoulos, C. Equation‐free, coarse‐grained multiscale computation: enabling mocroscopic simulators to perform system‐level analysis. Commun Math Sci 2003, 1:715–762.

Kevrekidis, IG, Gear, CW, Hummer, G. Equation‐free: the computer‐aided analysis of complex multiscale systems. AIChE J 2004, 50:1346–1355.

Coifman, RR, I. G. Kevrekidis,, S. Lafon,, M. Maggioni,, and B. Nadler,. Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems. Multiscale Model Simul 2008, 7:842–864.

Coifman, RR, Lafon, S, Lee, AB, Maggioni, M, Nadler, B, Warner, F, Zucker, SW. Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. Proc Natl Acad Sci USA 2005, 102:7426–7431.

Coifman, RR, Lafon, S, Lee, AB, Maggioni, M, Nadler, B, Warner, F, Zucker, SW. Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods. Proc Natl Acad Sci USA 2005, 102:7432–7437.

Moon, SJ, Cook, KA, Rajendran, K, Kevrekidis, IG, Cisternas, J, Laing, CR. Coarse‐grained clustering dynamics of heterogeneously coupled neurons. J Math Neurosci JMN 2015, 5:1–20.

Laing, CR, Frewen, TA, Kevrekidis, IG. Coarse‐grained dynamics of an activity bump in a neural field model. Nonlinearity 2007, 20:2127.

Wasylenko, TM, Cisternas, JE, Laing, CR, Kevrekidis, IG. Bifurcations of lurching waves in a thalamic neuronal network. Biol Cybern 2010, 103:447–462.

Marschler, C, Faust‐Ellsässer, C, Starke, J, van Hemmen, JL. Bifurcation of learning and structure formation in neuronal maps. EPL Europhys Lett 2014, 108:48005.

Laing, CR, Kevrekidis, IG. Equation‐free analysis of spike‐timing‐dependent plasticity. Biol Cybern 2015, 109:701–714.

Moon, SJ, Ghanem, R, Kevrekidis, IG. Coarse graining the dynamics of coupled oscillators. Phys Rev Lett 2006, 96:144101.

Laing, CR, Kevrekidis, IG. Periodically‐forced finite networks of heterogeneous globally‐coupled oscillators: a low‐dimensional approach. Phys Nonlinear Phenom 2008, 237:207–215.

Spiliotis, KG, Siettos, CI. Multiscale computations on neural networks: from the individual neuron interactions to the macroscopic‐level analysis. Int J Bifurc Chaos 2010, 20:121–134.

Spiliotis, KG, Siettos, CI. A timestepper‐based approach for the coarse‐grained analysis of microscopic neuronal simulators on networks: bifurcation and rare‐events micro‐ to macro‐computations. Neurocomputing 2011, 74:3576–3589.

Papo, D, Buldú, JM, Boccaletti, S, Bullmore, ET. Complex network theory and the brain. Phil Trans R Soc B 2014, 369:20130520.

Sporns, O, Tononi, G, Edelman, GM. Connectivity and complexity: the relationship between neuroanatomy and brain dynamics. Neural Netw Off J Int Neural Netw Soc 2000, 13:909–922.

Brazier, MA. Spread of seizure discharges in epilepsy: anatomical and electrophysiological considerations. Exp Neurol 1972, 36:263–272.

Gerstein, GL, Perkel, DH, Subramanian, KN. Identification of functionally related neural assemblies. Brain Res 1978, 140:43–62.

Zalesky, A, Fornito, A, Bullmore, E. On the use of correlation as a measure of network connectivity. Neuroimage 2012, 60:2096–2106.

Siggiridou, E, Kugiumtzis, D, Kimiskidis, VK. Correlation networks for identifying changes in brain connectivity during epileptiform discharges and transcranial magnetic stimulation. Sensors 2014, 14:12585–12597.

Seth, AK, Barrett, AB, Barnett, L. Granger causality analysis in neuroscience and neuroimaging. J Neurosci Off J Soc Neurosci 2015, 35:3293–3297.

Seth, AK. A MATLAB toolbox for Granger causal connectivity analysis. J Neurosci Methods 2010, 186:262–273.

Geweke, J. Measurement of linear dependence and feedback between multiple time series. J Am Stat Assoc 1982, 77:304–313.

Lachaux, JP, Rodriguez, E, Martinerie, J, et al. Measuring phase synchrony in brain signals. Hum Brain Mapp 1999, 8:194–208.

Stam, CJ, Nolte, G, Daffertshofer, A. Phase lag index: assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources. Hum Brain Mapp 2007, 28:1178–1193.

Vicente, R, Wibral, M, Lindner, M, Pipa, G. Transfer entropy—a model‐free measure of effective connectivity for the neurosciences. J Comput Neurosci 2010, 30:45–67.

Calhoun, VD, Adali, T, Pearlson, GD, Pekar, JJ. A method for making group inferences from functional MRI data using independent component analysis. Hum Brain Mapp 2001, 14:140–151.

Calhoun, VD, Liu, J, Adali, T. A review of group ICA for fMRI data and ICA for joint inference of imaging, genetic, and ERP data. Neuroimage 2009, 45:S163–S172.

Reidl, J, Starke, J, Omer, DB, et al. Independent component analysis of high‐resolution imaging data identifies distinct functional domains. Neuroimage 2007, 34:94–108.

Anderson, A, Cohen, MS. Decreased small‐world functional network connectivity and clustering across resting state networks in schizophrenia: an fMRI classification tutorial. Front Hum Neurosci 2013, 7:520.

Tenenbaum, JB, de Silva, V, Langford, JC. A global geometric framework for nonlinear dimensionality reduction. Science 2000, 290:2319–2323.

Duncan, D, Talmon, R, Zaveri, HP, Coifman, RR. Identifying preseizure state in intracranial EEG data using diffusion kernels. Math Biosci Eng MBE 2013, 10:579–590.

Keller, CJ, Bickel, S, Honey, CJ, Groppe, DM, Entz, L, Craddock, RC, Lado, FA, Kelly, C, Milham, M, Mehta, AD. Neurophysiological investigation of spontaneous correlated and anticorrelated fluctuations of the BOLD signal. J Neurosci Off J Soc Neurosci 2013, 33:6333–6342.

Megumi, F, Yamashita, A, Kawato, M, Imamizu, H, et al. Functional MRI neurofeedback training on connectivity between two regions induces long‐lasting changes in intrinsic functional network. Front Hum Neurosci 2015, 9:160.

Li, X, Wang, H. Identification of functional networks in resting state fMRI data using adaptive sparse representation and affinity propagation clustering. Front Neurosci 2015, 9. doi:10.3389/fnins.2015.00383.

Shaw, JC. Correlation and coherence analysis of the EEG: a selective tutorial review. Int J Psychophysiol Off J Int Organ Psychophysiol 1984, 1:255–266.

Al‐Aidroos, N, Said, CP, Turk‐Browne, NB. Top‐down attention switches coupling between low‐level and high‐level areas of human visual cortex. Proc Natl Acad Sci USA 2012, 109:14675–14680.

Florin, E, Gross, J, Pfeifer, J, Fink, GR, Timmermann, L. The effect of filtering on Granger causality based multivariate causality measures. Neuroimage 2010, 50:577–588.

Gao, Q, Duan, X, Chen, H. Evaluation of effective connectivity of motor areas during motor imagery and execution using conditional Granger causality. Neuroimage 2011, 54:1280–1288.

Liao, W, Ding, J, Marinazzo, D, Xu, Q, Wang, Z, Yuan, C, Zhang, Z, Lu, G, Chen, H. Small‐world directed networks in the human brain: multivariate Granger causality analysis of resting‐state fMRI. Neuroimage 2011, 54:2683–2694.

Miao, X, Wu, X, Li, R, Chen, K, Yao, L. Altered connectivity pattern of hubs in default‐mode network with Alzheimer`s disease: an Granger causality modeling approach. PLoS One 2011, 6:e25546.

Roebroeck, A, Formisano, E, Goebel, R. Mapping directed influence over the brain using Granger causality and fMRI. Neuroimage 2005, 25:230–242.

Sabatinelli, D, McTeague, LM, Dhamala, M, Frank, DW, Wanger, TJ, Adhikari, BM. Reduced medial prefrontal‐subcortical connectivity in dysphoria: Granger causality analyses of rapid functional magnetic resonance imaging. Brain Connect 2015, 5:1–9.

Tang, W, Bressler, SL, Sylvester, CM, Shulman, GL, Corbetta, M. Measuring Granger causality between cortical regions from voxelwise fMRI BOLD signals with LASSO. PLoS Comput Biol 2012, 8:e1002513.

Wu, GR, Liao, W, Stramaglia, S, Chen, H, Marinazzo, D. Recovering directed networks in neuroimaging datasets using partially conditioned Granger causality. Brain Connect 2013, 3:294–301.

Zhou, Z, Wang, X, Klahr, NJ, Liu, W, Arias, D, Liu, H, von Deneen, KM, Wen, Y, Lu, Z, Xu, D, et al. A conditional Granger causality model approach for group analysis in functional magnetic resonance imaging. Magn Reson Imaging 2011, 29:418–433.

Barrett, AB, Murphy, M, Bruno, MA, Noirhomme, Q, Boly, M, Laureys, S, Seth, AK. Granger causality analysis of steady‐state electroencephalographic signals during propofol‐induced anaesthesia. PLoS One 2012, 7:e29072.

Barnett, L, Seth, AK. Behaviour of Granger causality under filtering: theoretical invariance and practical application. J Neurosci Methods 2011, 201:404–419.

Gow, DW Jr, Segawa, JA, Ahlfors, SP, Lin, FH. Lexical influences on speech perception: a Granger causality analysis of MEG and EEG source estimates. Neuroimage 2008, 43:614–623.

Keil, A, Sabatinelli, D, Ding, M, Lang, PJ, Ihssen, N, Heim, S. Re‐entrant projections modulate visual cortex in affective perception: evidence from Granger causality analysis. Hum Brain Mapp 2009, 30:532–540.

Nicolaou, N, Hourris, S, Alexandrou, P, Georgiou, J. EEG‐based automatic classification of “awake” versus “anesthetized” state in general anesthesia using Granger causality. PLoS One 2012, 7:e33869.

de Tommaso, M, Stramaglia, S, Marinazzo, D, Trotta, G, Pellicoro, M. Functional and effective connectivity in EEG alpha and beta bands during intermittent flash stimulation in migraine with and without aura. Cephalalgia Int J Headache 2013, 33:938–947.

Protopapa, F, Siettos, CI, Evdokimidis, I, Smyrnis, N. Granger causality analysis reveals distinct spatio‐temporal connectivity patterns in motor and perceptual visuo‐spatial working memory. Front Comput Neurosci 2014, 8:146.

Protopapa, F, Siettos, CI, Myatchin, I, Lagae, L. Children with well controlled epilepsy possess different spatio‐temporal patterns of causal network connectivity during a visual working memory task. Cogn Neurodyn 2016, 10:1–13.

Kamiński, M, Ding, M, Truccolo, WA, Bressler, SL. Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance. Biol Cybern 2001, 85:145–157.

Baccalá, LA, Sameshima, K. Partial directed coherence: a new concept in neural structure determination. Biol Cybern 2001, 84:463–474.

Korzeniewska, A, Mańczak, M, Kamiński, M, Blinowska, KJ, Kasicki, S. Determination of information flow direction among brain structures by a modified directed transfer function (dDTF) method. J Neurosci Methods 2003, 125:195–207.

Winterhalder, M, Schelter, B, Hesse, W, Schwab, K, Leistritz, L, Klan, D, Bauer, R, Timmer, J, Witte, H. Comparison of linear signal processing techniques to infer directed interactions in multivariate neural systems. Signal Process 2005, 85:2137–2160.

Freiwald, WA, Valdes, P, Bosch, J, Biscay, R, Jimenez, JC, Rodriguez, LM, Rodriguez, V, Kreiter, AK, Singer, W. Testing non‐linearity and directedness of interactions between neural groups in the macaque inferotemporal cortex. J Neurosci Methods 1999, 94:105–119.

Marinazzo, D, Liao, W, Chen, H, Stramaglia, S. Nonlinear connectivity by Granger causality. Neuroimage 2011, 58:330–338.

Marinazzo, D, Pellicoro, M, Stramaglia, S. Nonlinear parametric model for Granger causality of time series. Phys Rev E 2006, 73:066216.

Trujillo, LT, Peterson, MA, Kaszniak, AW, Allen, JJ. EEG phase synchrony differences across visual perception conditions may depend on recording and analysis methods. Clin Neurophysiol Off J Int Fed Clin Neurophysiol 2005, 116:172–189.

Lopes da Silva, FH. Event‐related neural activities: what about phase? Prog Brain Res 2006, 159:3–17.

Schack, B, Weiss, S. Quantification of phase synchronization phenomena and their importance for verbal memory processes. Biol Cybern 2005, 92:275–287.

Kitzbichler, MG, Henson, RNA, Smith, ML, Nathan, PJ, Bullmore, ET. Cognitive effort drives workspace configuration of human brain functional networks. J Neurosci Off J Soc Neurosci 2011, 31:8259–8270.

Melloni, L, Molina, C, Pena, M, Torres, D, Singer, W, Rodriguez, E. Synchronization of neural activity across cortical areas correlates with conscious perception. J Neurosci Off J Soc Neurosci 2007, 27:2858–2865.

Gaillard, R, Dehaene, S, Adam, C, Clémenceau, S, Hasboun, D, Baulac, M, Cohen, L, Naccache, L. Converging intracranial markers of conscious access. PLoS Biol 2009, 7:e61.

Pockett, S, Bold, GEJ, Freeman, WJ. EEG synchrony during a perceptual‐cognitive task: widespread phase synchrony at all frequencies. Clin Neurophysiol Off J Int Fed Clin Neurophysiol 2009, 120:695–708.

Gross, J, Schmitz, F, Schnitzler, I, Kessler, K, Shapiro, K, Hommel, B, Schnitzler, A. Modulation of long‐range neural synchrony reflects temporal limitations of visual attention in humans. Proc Natl Acad Sci USA 2004, 101:13050–13055.

Rodriguez, E, George, N, Lachaux, JP, Martinerie, J, Renault, B, Varela, FJ. Perception`s shadow: long‐distance synchronization of human brain activity. Nature 1999, 397:430–433.

Mylonas, DS, Siettos, CI, Evdokimidis, I, Papanicolaou, AC, Smyrnis, N. Modular patterns of phase desynchronization networks during a simple visuomotor task. Brain Topogr 2016, 29:118–129.

Peraza, LR, Asghar, AU, Green, G, Halliday, DM. Volume conduction effects in brain network inference from electroencephalographic recordings using phase lag index. J Neurosci Methods 2012, 207:189–199.

Mormann, F, Lehnertz, K, David, P, Elger, CE. Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients. Phys Nonlinear Phenom 2000, 144:358–369.

Nolte, G, Ziehe, A, Nikulin, VV, et al. Robustly estimating the flow direction of information in complex physical systems. Phys Rev Lett 2008, 100:234101.

Vinck, M, Oostenveld, R, van Wingerden, M, Battaglia, F, Pennartz, CM. An improved index of phase‐synchronization for electrophysiological data in the presence of volume‐conduction, noise and sample‐size bias. Neuroimage 2011, 55:1548–1565.

Iasemidis, LD, Sackellares, JC, Zaveri, HP, Williams, WJ. Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures. Brain Topogr 1990, 2:187–201.

Iasemidis, L, Sabesan, S, Chakravarthy, N, Prasad, A, Tsakalis, K. %22Brain dynamics and modeling in epilepsy: prediction and control studies%22. In: Dana, SK, Roy, PK, Kurths, J, eds. Complex Dynamics in Physiological Systems: From Heart to Brain. The Netherlands: Springer; 2009, 185–214.

Senthilkumar, DV, Lakshmanan, M, Kurths, J. Transition from phase to generalized synchronization in time‐delay systems. Chaos Interdiscip J Nonlinear Sci 2008, 18:023118.

Pikovsky, A, Rosenblum, M, Kurths, J. Phase synchronization in regular and chaotic systems. Int J Bifurc Chaos 2000, 10:2291–2305.

Chávez, M, Martinerie, J, Le Van Quyen, M. Statistical assessment of nonlinear causality: application to epileptic EEG signals. J Neurosci Methods 2003, 124:113–128.

Ramanand, P, Bruce, MC, Bruce, EN. Mutual information analysis of EEG signals indicates age‐related changes in cortical interdependence during sleep in middle‐aged versus elderly women. J Clin Neurophysiol Off Publ Am Electroencephalogr Soc 2010, 27:274–284.

Wan, X, Crüts, B, Jensen, HJ. The causal inference of cortical neural networks during music improvisations. PLoS One 2014, 9:e112776. doi:10.1371/journal.pone.0112776.

Wibral, M, Vicente, R, Lizier, JT, eds. Directed Information Measures in Neuroscience. Berlin and Heidelberg: Springer; 2014.

Takens, F. %22Detecting strange attractors in turbulence%22. In: Rand, D, Young, L‐S, eds. Dynamical Systems and Turbulence, Warwick 1980. Berlin and Heidelberg: Springer; 1981, 366–381.

Pezard, L, Lachaux, JP, Thomasson, N, Martinerie, J. Why bother to spatially embed EEG? Comments on Pritchard et al., *Psychophysiology* 1996, 33: 362–368. Psychophysiology 1999, 36:527–531.

Sauer, T, Yorke, JA, Casdagli, M. Embedology. J Stat Phys 1991, 65:579–616.

Papana, A, Kyrtsou, C, Kugiumtzis, D, Diks, C. Simulation study of direct causality measures in multivariate time series. Entropy 2013, 15:2635–2661.

Friston, KJ, Frith, CD, Liddle, PF, Frackowiak, RS. Functional connectivity: the principal‐component analysis of large (PET) data sets. J Cereb Blood Flow Metab 1993, 13:5–14.

Li, K, Guo, L, Nie, J, Li, G, Liu, T. Review of methods for functional brain connectivity detection using fMRI. Comput Med Imaging Graph Off J Comput Med Imaging Soc 2009, 33:131–139.

Leonardi, N, Richiardi, J, Gschwind, M, Simioni, S, Annoni, JM, Schluep, M, Vuilleumier, P, Van De Ville, D. Principal components of functional connectivity: a new approach to study dynamic brain connectivity during rest. Neuroimage 2013, 83:937–950.

Anderson, A, Dinov, ID, Sherin, JE, Quintana, J, Yuille, AL, Cohen, MS. Classification of spatially unaligned fMRI scans. Neuroimage 2010, 49:2509–2519.

Hyvärinen, A, Oja, E. Independent component analysis: algorithms and applications. Neural Netw Off J Int Neural Netw Soc 2000, 13:411–430.

Pruim, RH, Mennes, M, van Rooij, D, Llera, A, Buitelaar, JK, Beckmann, CF. ICA‐AROMA: a robust ICA‐based strategy for removing motion artifacts from fMRI data. Neuroimage 2015, 112:267–277.

Robinson, SD, Schöpf, V. ICA of fMRI studies: new approaches and cutting edge applications. Front Hum Neurosci 2013, 7:724.

McKeown, MJ, Jung, TP, Makeig, S, Brown, G, Kindermann, SS, Lee, TW, Sejnowski, TJ. Spatially independent activity patterns in functional MRI data during the stroop color‐naming task. Proc Natl Acad Sci USA 1998, 95:803–810.

McKeown, MJ, Hansen, LK, Sejnowsk, TJ. Independent component analysis of functional MRI: what is signal and what is noise? Curr Opin Neurobiol 2003, 13:620–629.

Jamadar, S, Egan, G, Calhoun, VD, Johnson, B, Fielding, J. Intrinsic connectivity provides the baseline framework for variability in motor performance: a multivariate fusion analysis of low‐ and high‐frequency resting‐state oscillations and antisaccade performance. Brain Connect 2016. doi:10.1089/brain.2015.0411.

Bär, KJ, de la Cruz, F, Schumann, A, Koehler, S, Sauer, H, Critchley, H, Wagner, G. Functional connectivity and network analysis of midbrain and brainstem nuclei. Neuroimage 2016, 134:53–63.

Cassidy, CM, Van Snellenberg, JX, Benavides, C, Slifstein, M, Wang, Z, Moore, H, Abi‐Dargham, A, Horga, G. Dynamic connectivity between brain networks supports working memory: relationships to dopamine release and schizophrenia. J Neurosci Off J Soc Neurosci 2016, 36:4377–4388.

Verma, R, Khurd, P, Davatzikos, C. On analyzing diffusion tensor images by identifying manifold structure using isomaps. IEEE Trans Med Imaging 2007, 26:772–778.

Kortelainen, J, Vayrynen, E, Seppanen, T. Isomap approach to EEG‐based assessment of neurophysiological changes during anesthesia. IEEE Trans Neural Syst Rehabil Eng Publ IEEE Eng Med Biol Soc 2011, 19:113–120.

Ye, AQ, Ajilore, OA, Conte, G, GadElkarim, J, Thomas‐Ramos, G, Zhan, L, Yang, S, Kumar, A, Magin, RL, Forbes, AG, et al. The intrinsic geometry of the human brain connectome. Brain Inform 2015, 2:197–210.

Richiardi, J, Achard, S, Bunke, H, Van De Ville, D. Machine learning with brain graphs: predictive modeling approaches for functional imaging in systems neuroscience. IEEE Signal Process Mag 2013, 30:58–70.

Becker, R, Knock, S, Ritter, P, Jirsa, V. Relating alpha power and phase to population firing and hemodynamic activity using a thalamo‐cortical neural mass model. PLoS Comput Biol 2015, 11:e1004352.

McCarthy, MM, Moore‐Kochlacs, C, Gu, X, Boyden, ES, Han, X, Kopell, N. Striatal origin of the pathologic beta oscillations in Parkinson`s disease. Proc Natl Acad Sci USA 2011, 108:11620–11625.

Dovzhenok, A, Rubchinsky, LL. On the origin of tremor in Parkinson`s disease. PLoS One 2012, 7:e41598.

Sarbaz, Y, Pourakbari, H. A review of presented mathematical models in Parkinson`s disease: black‐ and gray‐box models. Med Biol Eng Comput 2015, 54:855–868. doi:10.1007/s11517-015-1401-9.

Qi, Z, Miller, GW, Voit, EO. A mathematical model of presynaptic dopamine homeostasis: implications for schizophrenia. Pharmacopsychiatry 2008, 41(Suppl 1):S89–S98.

González‐Ramírez, LR, Ahmed, OJ, Cash, SS, Wayne, CE, Kramer, MA. A biologically constrained, mathematical model of cortical wave propagation preceding seizure termination. PLoS Comput Biol 2015, 11:e1004065.

Stefanescu, RA, Shivakeshavan, RG, Talathi, SS. Computational models of epilepsy. Seizure 2012, 21:748–759.

Friston, KJ, Harrison, L, Penny, W. Dynamic causal modelling. Neuroimage 2003, 19:1273–1302.

Stephan, KE, Penny, WD, Moran, RJ, den Ouden, HE, Daunizeau, J, Friston, KJ. Ten simple rules for dynamic causal modeling. Neuroimage 2010, 49:3099–3109.

Moran, R, Pinotsis, DA, Friston, K. Neural masses and fields in dynamic causal modeling. Front Comput Neurosci 2013, 7:57.

Youssofzadeh, V, Prasad, G, Fagan, AJ, Reilly, RB, Martens, S, Meaney, JF, Wong‐Lin, K. Signal propagation in the human visual pathways: an effective connectivity analysis. J Neurosci Off J Soc Neurosci 2015, 35:13501–13510.

Nguyen, VT, Breakspear, M, Hu, X, Guo, CC. The integration of the internal and external milieu in the insula during dynamic emotional experiences. Neuroimage 2016, 124:455–463.

Fastenrath, M, Coynel, D, Spalek, K, Milnik, A, Gschwind, L, Roozendaal, B, Papassotiropoulos, A, de Quervain, DJ. Dynamic modulation of amygdala‐hippocampal connectivity by emotional arousal. J Neurosci Off J Soc Neurosci 2014, 34:13935–13947.

Guhn, A, Domschke, K, Müller, LD, Dresler, T, Eff, F, Kopf, J, Deckert, J, Reif, A, Herrmann, MJ. Neuropeptide S receptor gene variation differentially modulates fronto‐limbic effective connectivity in childhood and adolescence. Cereb Cortex 2015, 10:1730–7. doi:10.1093/cercor/bhv259.

Gilbert, JR, Symmonds, M, Hanna, MG, Dolan, RJ, Friston, KJ, Moran, RJ. Profiling neuronal ion channelopathies with non‐invasive brain imaging and dynamic causal models: case studies of single gene mutations. Neuroimage 2016, 124:43–53.

Musgrove, DR, Eberly, LE, Klimes‐Dougan, B, Basgoze, Z3, Thomas, KM, Mueller, BA, Houri, A, Lim, KO, Cullen, KR. Impaired bottom‐Up effective connectivity between amygdala and subgenual anterior cingulate cortex in unmedicated adolescents with major depression: results from a dynamic causal modeling analysis. Brain Connect 2015, 5:608–619.

Cui, LB, Liu, J, Wang, LX, Li, C, Xi, YB, Guo, F, Wang, HN, Zhang, LC, Liu, WM, He, H, Tian, P, Yin, H, Lu, H. Anterior cingulate cortex‐related connectivity in first‐episode schizophrenia: a spectral dynamic causal modeling study with functional magnetic resonance imaging. Front Hum Neurosci 2015, 9:589.

Herz, DM, Siebner, HR, Hulme, OJ, Florin, E, Christensen, MS, Timmermann, L. Levodopa reinstates connectivity from prefrontal to premotor cortex during externally paced movement in Parkinson`s disease. Neuroimage 2014, 90:15–23.

Breakspear, M, Roberts, G, Green, MJ, Nguyen, VT, Frankland, A, Levy, F, Lenroot, R, Mitchell, PB. Network dysfunction of emotional and cognitive processes in those at genetic risk of bipolar disorder. Brain J Neurol 2015, 138:3427–3439.

Stephan, KE, Friston, KJ. Analyzing effective connectivity with fMRI. Wiley Interdiscip Rev Cogn Sci 2010, 1:446–459.

Hawkins, J, Ahmad, S. Why Neurons Have Thousands of Synapses, a Theory of Sequence Memory in Neocortex. Front. Neural Circuits 2016, doi:10.3389/fncir.2016.00023.