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.
Citation
Changjin Xu. "Neimark-Sacker Bifurcation Analysis for a Discrete-Time System of Two Neurons." Abstr. Appl. Anal. 2012 1 - 16, 2012. https://doi.org/10.1155/2012/546356
Information