Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons

Changjin Xu

Abstract and Applied Analysis, 2012, vol. 2012, 1-16

Abstract:

A class of discrete-time system modelling a network with two neurons is considered. First, we investigate the global stability of the given system. Next, we study the local stability by techniques developed by Kuznetsov to discrete-time systems. It is found that Neimark-Sacker bifurcation (or Hopf bifurcation for map) will occur when the bifurcation parameter exceeds a critical value. A formula determining the direction and stability of Neimark-Sacker bifurcation by applying normal form theory and center manifold theorem is given. Finally, some numerical simulations for justifying the theoretical results are also provided.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:546356

DOI: 10.1155/2012/546356

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