scholarpedia logo Izhikevich E.M. (Editor-in-Chief)
Scholarpedia , the free peer reviewed encyclopedia.
my new book Izhikevich E.M. (2007)
Dynamical Systems in Neuroscience:
The Geometry of Excitability and Bursting.

The MIT press
my book Hoppensteadt F.C. and Izhikevich E.M. (1997)
Weakly Connected Neural Networks.

Springer-Verlag, New York
Articles:
Izhikevich E. M. (2010)
Hybrid Spiking Models.
Phil. Trans. R. Soc. A 368:5061-5070
Szatmary B. and Izhikevich E. M. (2010)
Spike-Timing Theory of Working Memory.
PLoS Computational Biology, 6(8): e1000879
Izhikevich E. M. and Hoppensteadt F.C. (2009)
Polychronous Wavefront Computations.
International Journal of Bifurcation and Chaos, 19:1733-1739
Izhikevich E. M. and Edelman G. M. (2008) 
Large-Scale Model of Mammalian Thalamocortical Systems.
PNAS, 105:3593-3598
Izhikevich E. M. and Ermentrout G. B. (2008)
Phase model.
Scholarpedia, 3(10):1487
Terman D. H. and Izhikevich E. M. (2008)
State space.
Scholarpedia, 3(3):1924
Izhikevich E.M. (2007) 
Solving the Distal Reward Problem through Linkage of STDP and Dopamine Signaling.
Cerebral Cortex, 17:2443--2452 (10.1093/cercor/bhl152)
Izhikevich E.M. (2007) 
Equilibrium.
Scholarpedia, 2(10):2014
Seth A. K., Izhikevich E., Reeke G.N., and Edelman G.M. (2006) 
Theories and measures of consciousness: An extended framework.
PNAS, 10.1073/pnas.0604347103.
Izhikevich E.M. and FitzHugh R. (2006) 
FitzHugh-Nagumo Model.
Scholarpedia, 1:(9)1349
Izhikevich E.M. and Kuramoto Y. (2006) 
Weakly Coupled Oscillators.
Encyclopedia of Mathematical Physics, Elsevier, 5:448
Izhikevich E.M.(2006) 
Bursting.
Scholarpedia, 1(3):1300
Izhikevich E.M. (2006) 
Polychronization: Computation With Spikes.
Neural Computation,18:245-282
Wu N., Enomoto A., Tanaka S., Hsiao C.-F., Nykamp D.Q., Izhikevich E., and Chandler S.H. (2005) 
Persistent Sodium Currents in Mesencephalic V Neurons Participate in Burst Generation and Control of Membrane Excitability
Journal of Neurophysiology 93:2710--2722
Izhikevich E.M. (2004) 
Which Model to Use for Cortical Spiking Neurons?
IEEE Transactions on Neural Networks, 15:1063-1070 (special issue on temporal coding)
Izhikevich E.M. and Hoppensteadt F.C. (2004) 
Classification of Bursting Mappings.
International Journal of Bifurcation and Chaos, 14:3847-3854
Izhikevich E.M., Gally J.A., and Edelman, G.M. (2004) 
Spike-Timing Dynamics of Neuronal Groups.
Cerebral Cortex, 14:933-944
Izhikevich E.M. (2003) 
Simple Model of Spiking Neurons.
IEEE Transactions on Neural Networks, 14:1569- 1572
Izhikevich E.M. and Hoppensteadt F.C. (2003) 
Slowly Coupled Oscillators: Phase Dynamics and Synchronization.
SIAM Journal on Applied Mathematics, 63:1935-1953
Izhikevich E.M. and Desai N.S. (2003) 
Relating STDP to BCM.
Neural Computation 15:15111523
Izhikevich E.M., Desai N.S., Walcott E.C., Hoppensteadt F.C. (2003) 
Bursts as a unit of neural information: selective communication via resonance.
Trends in Neuroscience 26:161-167
Izhikevich E.M. (2002) 
Resonance and Selective Communication Via Bursts in Neurons Having Subthreshold Oscillations.
BioSystems, 67:95-102
Hoppensteadt F.C. and Izhikevich E.M. (2002) 
Canonical Neural Models. 
In Arbib MA (Ed) Brain Theory and Neural Networks. Second Edition. The MIT press, Cambridge, MA, pages 181-186. (Invited review paper)
Izhikevich E.M. (2001) 
Synchronization of Elliptic Bursters.
SIAM Review, 43:315-344
(Featured SIGEST paper selected on the basis of its exceptional interest to the entire SIAM community.)
Izhikevich E.M. (2001) 
Resonate-and-Fire Neurons.
Neural Networks, 14:883-894
Hoppensteadt F.C. and Izhikevich E.M. (2001) 
Synchronization of MEMS Resonators and Mechanical Neurocomputing. 
IEEE Transactions On Circuits and Systems I, 48:133-138
Hoppensteadt F.C. and Izhikevich E.M. (2000) 
Synchronization of Laser Oscillators, Associative Memory, and Optical Neurocomputing.
Physical Review E, 62:4010-4013
Hoppensteadt F.C. and Izhikevich E.M. (2000) 
Pattern Recognition Via Synchronization in Phase-Locked Loop Neural Networks. 
IEEE Transactions On Neural Networks, 11:734-738
Izhikevich E.M. (2000) 
Phase Equations For Relaxation Oscillators.
SIAM Journal on Applied Mathematics, 60:1789-1805
Izhikevich E.M. (2000) 
Neural Excitability, Spiking, and Bursting.
International Journal of Bifurcation and Chaos. 10:1171-1266. 
(Long review/tutorial paper with 126 illustrations.)
Izhikevich E.M. (2000) 
Subcritical Elliptic Bursting of Bautin Type.
SIAM Journal on Applied Mathematics, 60:503-535
Izhikevich E.M. (1999) 
Weakly Connected Quasiperiodic Oscillators, FM Interactions, and Multiplexing in the Brain.
SIAM Journal on Applied Mathematics, 59:2193-2223
Hoppensteadt F.C. and Izhikevich E.M. (1999) 
Oscillatory Neurocomputers With Dynamic Connectivity.
Physical Review Letters 82:2983-2986
Izhikevich E.M. (1999) 
Class 1 Neural Excitability, Conventional Synapses, Weakly Connected Networks, and Mathematical Foundations of Pulse-Coupled Models.
IEEE Transactions On Neural Networks,10:499-507
Izhikevich E.M. (1999) 
Weakly Pulse-Coupled Oscillators, FM Interactions, Synchronization, and Oscillatory Associative Memory.
IEEE Transactions On Neural Networks, 10:508-526(Review/tutorial paper)
Hoppensteadt F.C. and Izhikevich E.M. (1998) 
Thalamo-Cortical Interactions Modeled by Weakly Connected Oscillators: Could Brain Use FM Radio Principles?
BioSystems, 48:85-94
Izhikevich E.M. (1998) 
Phase Models With Explicit Time Delays.
Physical Review E, 58:905-908
Izhikevich E.M. (1998) 
Multiple Cusp Bifurcations.
Neural Networks, 11:495-508
Hoppensteadt F.C. and Izhikevich E.M. (1996) 
Synaptic Organizations and Dynamical Properties of Weakly Connected Neural Oscillators. II. Learning of Phase Information.
Biological Cybernetics, 75:129--135
Hoppensteadt F.C. and Izhikevich E.M. (1996) 
Synaptic Organizations and Dynamical Properties of Weakly Connected Neural Oscillators: I. Analysis of Canonical Model
Biological Cybernetics, 75:117--127
Izhikevich E.M. and Malinetskii G.G. (1993) 
A Neural Network With Chaotic Behavior.
Neurocomputers (in Russian)
Izhikevich E.M. and MalinetskiiG.G. (1992) 
A Possible Role of Chaos in Neurosystems
Dokl. Akad. Nauk SSSR, 326:626-632 (translated in Sov. Phys. Docl. (1993) 37(10) October 1992:492--495)
Izhikevich E.M., Mikhailov A.S., and Sveshnikov N.A. (1991) 
Memory, Learning and Neuromediators.
BioSystems, 25:219-230
Animated Talks:
Phase Dynamics and Synchronization of Relaxation Oscillators
Sixth SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, May 2001 
(A Powerpoint presentation with MATLAB animations)
The Neuron as a Nonlinear Resonator
Workshop "The Neuron as a Nonlinear Oscillator", Salk Institute, La Jolla, CA, August, 2000 
(A Powerpoint presentation with MATLAB animations)
Synchronization of Bursters
SIAM Pacific Rim Dynamical Systems Conference, Hawaii, August, 2000 
(A Powerpoint presentation with MATLAB animations)
Patents:
Hoppensteadt F.C. and Izhikevich E.M. 
PLL Oscillatory Neurocomputer.
Provisional Patent Application, USPTO.
Hoppensteadt F.C. and Izhikevich E.M. 
Mechanical Computation With MEMS Resonators.
Provisional Patent Application, USPTO, Serial Number 60/178,654.
Hoppensteadt F.C. and Izhikevich E.M. 
Optical Computation Via Phase Modulation of Laser Oscillators.
Provisional Patent Application, USPTO.
Hoppensteadt F.C. and Izhikevich E.M. 
Oscillatory Neurocomputers With Dynamic Connectivity.
Provisional Patent Application for Letters Patent of the United States, Serial No. 60/108,353.
 
 

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