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Savitribai Phule Pune University All Models Are False, Some Are Useful

Technical Report CMS-TR-20061009


Title Synchronization in a Network of Model Neurons
Author/s Maruthi Pradeep Kanth Jampa
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India


Abhijeet R. Sonawane, Prashant M. Gade
Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411 007 India


Sudeshna Sinha
The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India
Abstract We study the spatiotemporal dynamics of a network of coupled chaotic maps modelling neuronal activity, under variation of coupling strength epsilon and degree of randomness in coupling p. We find that at high coupling strengths (epsilon>epsilonfixed) the unstable saddle point solution of the local chaotic maps gets stabilized. The range of coupling where this spatiotemporal fixed point gains stability is unchanged in the presence of randomness in the connections, namely epsilonfixed is invariant under changes in p. As coupling gets weaker (epsilon<epsilonfixed), the spatiotemporal fixed point loses stability, and one obtains chaos. In this regime, when the coupling connections are completely regular (p=0), the network becomes spatiotemporally chaotic. Interestingly however, in the presence of random links (p>0) one obtains spatial synchronization in the network. We find that this range of synchronized chaos increases exponentially with the fraction of random links in the network. Further, in the space of fixed coupling strengths, the synchronization transition occurs at a finite value of p, a scenario quite distinct from the many examples of synchronization transitions at p-->0. Further we show that the synchronization here is robust in the presence of parametric noise, namely in a network of nonidentical neuronal maps. Finally we check the generality of our observations in networks of neurons displaying both spiking and bursting dynamics.
Keywords
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Citing This Document Maruthi Pradeep Kanth Jampa, Abhijeet R. Sonawane, Prashant M. Gade, and Sudeshna Sinha , Synchronization in a Network of Model Neurons . Technical Report CMS-TR-20061009 of the Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411007, India (2006); available at http://cms.unipune.ernet.in/reports/.
Notes, Published Reference, Etc. Published as Physical Review E 75, 026215 (2007)
Contact gade AT cms.unipune.ernet.in
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