Neimark‐Sacker Bifurcation Analysis for a Discrete‐Time System of Two Neurons
Changjin Xu · Abstract and Applied Analysis · 2012
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.