Bifurcation and oscillation in a time-delay neural mass model

[1]  Frank Marten,et al.  Characterising the dynamics of EEG waveforms as the path through parameter space of a neural mass model: Application to epilepsy seizure evolution , 2012, NeuroImage.

[2]  Olivier D. Faugeras,et al.  Neural Mass Activity, Bifurcations, and Epilepsy , 2011, Neural Computation.

[3]  Stephen Coombes,et al.  Large-scale neural dynamics: Simple and complex , 2010, NeuroImage.

[4]  Olivier D. Faugeras,et al.  A Markovian event-based framework for stochastic spiking neural networks , 2009, Journal of Computational Neuroscience.

[5]  Karl J. Friston,et al.  Dynamic causal modeling for EEG and MEG , 2009, Human brain mapping.

[6]  Karl J. Friston,et al.  Bayesian estimation of synaptic physiology from the spectral responses of neural masses , 2008, NeuroImage.

[7]  Karl J. Friston,et al.  The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields , 2008, PLoS Comput. Biol..

[8]  P. Robinson,et al.  Modeling absence seizure dynamics: implications for basic mechanisms and measurement of thalamocortical and corticothalamic latencies. , 2008, Journal of theoretical biology.

[9]  Viktor K. Jirsa,et al.  A Low Dimensional Description of Globally Coupled Heterogeneous Neural Networks of Excitatory and Inhibitory Neurons , 2008, PLoS Comput. Biol..

[10]  Viktor K. Jirsa,et al.  Dispersion and time delay effects in synchronized spike–burst networks , 2008, Cognitive Neurodynamics.

[11]  Lutz Schimansky-Geier,et al.  Implications of heterogeneous inputs and connectivity on the synchronization in excitable networks , 2008 .

[12]  Karl J. Friston,et al.  Variational Bayesian inversion of the equivalent current dipole model in EEG/MEG , 2008, NeuroImage.

[13]  Sharene D. Bungay,et al.  Patterns of oscillation in a Ring of Identical Cells with Delayed Coupling , 2007, Int. J. Bifurc. Chaos.

[14]  Karl J. Friston,et al.  Dynamic causal modelling of evoked potentials: A reproducibility study , 2007, NeuroImage.

[15]  Yuan Yuan,et al.  Dynamics in a delayed-neural network , 2007 .

[16]  Farran Briggs,et al.  A Fast, Reciprocal Pathway between the Lateral Geniculate Nucleus and Visual Cortex in the Macaque Monkey , 2007, The Journal of Neuroscience.

[17]  Lihong Huang,et al.  Stability of nonlinear waves in a ring of neurons with delays , 2007 .

[18]  Olivier D. Faugeras,et al.  Bifurcation Analysis of Jansen's Neural Mass Model , 2006, Neural Computation.

[19]  Karl J. Friston,et al.  Dynamic causal modeling of evoked responses in EEG and MEG , 2006, NeuroImage.

[20]  Karl J. Friston,et al.  Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization , 2006, NeuroImage.

[21]  S. Bungay,et al.  Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling , 2005 .

[22]  Shangjiang Guo Spatio-temporal patterns of nonlinear oscillations in an excitatory ring network with delay , 2005 .

[23]  M. Sirota,et al.  Three Channels of Corticothalamic Communication during Locomotion , 2005, The Journal of Neuroscience.

[24]  Junjie Wei,et al.  Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays , 2005 .

[25]  M. Velarde,et al.  Bifurcation analysis and existence of periodic solutions in a simple neural network with delays. , 2004, Chaos.

[26]  P A Robinson,et al.  Estimation of multiscale neurophysiologic parameters by electroencephalographic means , 2004, Human brain mapping.

[27]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .

[28]  S. A. Campbell,et al.  Stability and Synchronization of a Ring of Identical Cells with Delayed Coupling , 2004 .

[29]  J A Scott Kelso,et al.  Synchrony and clustering in heterogeneous networks with global coupling and parameter dispersion. , 2004, Physical review letters.

[30]  Karl J. Friston,et al.  A neural mass model for MEG/EEG: coupling and neuronal dynamics , 2003, NeuroImage.

[31]  T. Tsumoto,et al.  Change of conduction velocity by regional myelination yields constant latency irrespective of distance between thalamus and cortex , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[32]  B. Connors,et al.  Short-term dynamics of thalamocortical and intracortical synapses onto layer 6 neurons in neocortex. , 2002, Journal of neurophysiology.

[33]  S. De Monte,et al.  Coherent regimes of globally coupled dynamical systems. , 2002, Physical review letters.

[34]  Lee M. Miller,et al.  Functional Convergence of Response Properties in the Auditory Thalamocortical System , 2001, Neuron.

[35]  P. Golshani,et al.  Differentiation of corticothalamic and collateral thalamocortical synapses on mouse reticular nucleus neurons by EPSC amplitude and AMPA receptor subunit composition , 2001 .

[36]  Fabrice Wendling,et al.  Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals , 2000, Biological Cybernetics.

[37]  L. F Abbott,et al.  Lapicque’s introduction of the integrate-and-fire model neuron (1907) , 1999, Brain Research Bulletin.

[38]  Y. Kuznetsov Elements of applied bifurcation theory (2nd ed.) , 1998 .

[39]  Dirk Roose,et al.  COMPUTATION, CONTINUATION AND BIFURCATION ANALYSIS OF PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS , 1997 .

[40]  Dirk Roose,et al.  Numerical stability analysis and computation of Hopf bifurcation points for delay differential equations , 1996 .

[41]  Ben H. Jansen,et al.  Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns , 1995, Biological Cybernetics.

[42]  J. Tepper,et al.  Cerebellar-responsive neurons in the thalamic ventroanterior-ventrolateral complex of rats: In vivo electrophysiology , 1994, Neuroscience.

[43]  R. Seydel Practical Bifurcation and Stability Analysis , 1994 .

[44]  Mitchell Glickstein,et al.  Foundations of the neuron doctrine , 1993, Medical History.

[45]  Walter J. Freeman,et al.  Asymmetric sigmoid non-linearity in the rat olfactory system , 1991, Brain Research.

[46]  W. Freeman Simulation of chaotic EEG patterns with a dynamic model of the olfactory system , 1987, Biological Cybernetics.

[47]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[48]  H. Swadlow,et al.  Efferent systems of the rabbit visual cortex: Laminar distribution of the cells of origin, axonal conduction velocities, and identification of axonal branches , 1981, The Journal of comparative neurology.

[49]  T. Tsumoto,et al.  Three groups of cortico‐geniculate neurons and their distribution in binocular and monocular segments of cat striate cortex , 1980, The Journal of comparative neurology.

[50]  O. D. Creutzfeldt,et al.  Functional organization of the corticofugal system from visual cortex to lateral geniculate nucleus in the cat , 1978, Experimental Brain Research.

[51]  J. Stone,et al.  Properties of relay cells in cat's lateral geniculate nucleus: a comparison of W-cells with X- and Y-cells. , 1976, Journal of neurophysiology.

[52]  F. H. Lopes da Silva,et al.  Model of brain rhythmic activity , 1974, Kybernetik.

[53]  R. L. Beurle Properties of a mass of cells capable of regenerating pulses , 1956, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[54]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[55]  Viktor K. Jirsa,et al.  Connectivity and dynamics of neural information processing , 2007, Neuroinformatics.

[56]  Ben H. Jansen,et al.  A neurophysiologically-based mathematical model of flash visual evoked potentials , 2004, Biological Cybernetics.

[57]  Pauline van den Driessche,et al.  Delayed Coupling Between Two Neural Network Loops , 2004, SIAM J. Appl. Math..

[58]  H. Swadlow Fast-spike interneurons and feedforward inhibition in awake sensory neocortex. , 2003, Cerebral cortex.

[59]  J. A. Kuznecov Elements of applied bifurcation theory , 1998 .

[60]  Stanley Finger,et al.  Origins of neuroscience: A history of explorations into brain function. , 1994 .

[61]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990, Bulletin of mathematical biology.

[62]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[63]  Pak Chiu Leung,et al.  Numerical bifurcation analysis of delay differential equations , 1982 .

[64]  W. Freeman Models of the dynamics of neural populations. , 1978, Electroencephalography and clinical neurophysiology. Supplement.

[65]  Freeman Wj Models of the dynamics of neural populations. , 1978 .

[66]  F. H. Lopes da Silva,et al.  Models of neuronal populations: the basic mechanisms of rhythmicity. , 1976, Progress in brain research.