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

Changjin Xu | Zendy

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

Author(s) -

Changjin Xu

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/546356

Subject(s) - mathematics , center manifold , bifurcation diagram , saddle node bifurcation , transcritical bifurcation , bifurcation , discrete time and continuous time , period doubling bifurcation , stability (learning theory) , biological applications of bifurcation theory , hopf bifurcation , mathematical analysis , nonlinear system , statistics , computer science , physics , quantum mechanics , machine learning

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

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