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

Abstract EN

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.