Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays | Zendy

Zizhen Zhang | Zendy; Huizhong Yang | Zendy

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Hopf Bifurcation Analysis for a Four-Dimensional Recurrent Neural Network with Two Delays

Author(s) -

Zizhen Zhang,

Huizhong Yang

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/436254

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

A four-dimensional recurrent neural network with two delays is considered. The main result is given in terms of local stability and Hopf bifurcation. Sufficient conditions for local stability of the zero equilibrium and existence of the Hopf bifurcation with respect to both delays are obtained by analyzing the distribution of the roots of the associated characteristic equation. In particular, explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form theory and center manifold theory. Some numerical examples are also presented to verify the theoretical analysis

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