Synchronization in network motifs of delay-coupled map-based neurons

Abstract We study the influence of delayed coupling on synchronization in neural network motifs. Numerical simulations based on the Rulkov map reveal different behavior in the presence and in the absence of the delay. While without delay, synchronization improves as the coupling strength is increased, in the presence of a delay, synchronization becomes worse. We also study how a feedback loop affects synchronization. An increase in the number of neurons involved in the loop leads to desynchronization in the motifs, saturating at a certain value of the synchronization index.

[1]  Z. Duan,et al.  Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Jürgen Kurths,et al.  Spatiotemporal Coherence Resonance in a Map Lattice , 2009, Int. J. Bifurc. Chaos.

[3]  Vito Latora,et al.  Synchronization properties of network motifs , 2006, physics/0609126.

[4]  Guanrong Chen,et al.  Synchronous Bursts on Scale-Free Neuronal Networks with Attractive and Repulsive Coupling , 2010, PloS one.

[5]  Martin Hasler,et al.  Synchronization of bursting neurons: what matters in the network topology. , 2005, Physical review letters.

[6]  C Mayol,et al.  Anticipated synchronization and the predict-prevent control method in the FitzHugh-Nagumo model system. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  H. Abarbanel,et al.  The role of chaos in neural systems , 1998, Neuroscience.

[8]  Igor Franović,et al.  Power law behavior related to mutual synchronization of chemically coupled map neurons , 2010 .

[9]  N. Rulkov.  Regularization of synchronized chaotic bursts. , 2000, Physical review letters.

[10]  J. M. Sausedo-Solorio,et al.  Synchronization of map-based neurons with memory and synaptic delay , 2014 .

[11]  R. Llinás.  I of the Vortex: From Neurons to Self , 2000 .

[12]  A. Selverston,et al.  Synchronous Behavior of Two Coupled Biological Neurons , 1998, chao-dyn/9811010.

[13]  Jürgen Kurths,et al.  Phase synchronization of chaotic intermittent oscillations. , 2004, Physical review letters.

[14]  Dante R. Chialvo,et al.  Generic excitable dynamics on a two-dimensional map , 1995 .

[15]  S. Shen-Orr,et al.  Network motifs in the transcriptional regulation network of Escherichia coli , 2002, Nature Genetics.

[16]  Osame Kinouchi,et al.  MODELING NEURONS BY SIMPLE MAPS , 1996 .

[17]  Claudio R Mirasso,et al.  Anticipated synchronization in a biologically plausible model of neuronal motifs. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  A. Selverston,et al.  Pacemaker and network mechanisms of rhythm generation: cooperation and competition. , 2008, Journal of theoretical biology.

[19]  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.

[20]  Andrey Shilnikov,et al.  Polyrhythmic synchronization in bursting networking motifs. , 2008, Chaos.

[21]  Nikolai F. Rulkov,et al.  Subthreshold oscillations in a map-based neuron model , 2004, q-bio/0406007.

[22]  Sergi Valverde,et al.  Network motifs in computational graphs: a case study in software architecture. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Qishao Lu,et al.  Bursting and synchronization transition in the coupled modified ML neurons , 2008 .

[24]  André Longtin,et al.  A two-variable model of somatic-dendritic interactions in a bursting neuron , 2002, Bulletin of mathematical biology.

[25]  A. Selverston,et al.  Inhibitory synchronization of bursting in biological neurons: dependence on synaptic time constant. , 2002, Journal of neurophysiology.

[26]  Nikolai F. Rulkov,et al.  Oscillations in Large-Scale Cortical Networks: Map-Based Model , 2004, Journal of Computational Neuroscience.

[27]  D. Amit.  The Hebbian paradigm reintegrated: Local reverberations as internal representations , 1995, Behavioral and Brain Sciences.

[28]  Frank C. Hoppensteadt,et al.  Classification of bursting Mappings , 2004, Int. J. Bifurc. Chaos.

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

[30]  B. Katz,et al.  The measurement of synaptic delay, and the time course of acetylcholine release at the neuromuscular junction , 1965, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[31]  O. Kinouchi,et al.  Stability diagrams for bursting neurons modeled by three-variable maps , 2004, q-bio/0402031.

[32]  Nikolai F Rulkov,et al.  Modeling of spiking-bursting neural behavior using two-dimensional map. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Antônio C. Roque-da-Silva,et al.  A minimal model for excitable and bursting elements , 2001, Neurocomputing.

[34]  Jürgen Kurths,et al.  Phase synchronization in noise-driven bursting neurons. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Andrey Shilnikov,et al.  Origin of Chaos in a Two-Dimensional Map Modeling Spiking-bursting Neural Activity , 2003, Int. J. Bifurc. Chaos.

[36]  Gerda de Vries,et al.  Bursting as an emergent phenomenon in coupled chaotic maps. , 2001 .