Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms | Zendy

Changjin Xu | Zendy; Xiaofei He | Zendy

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Stability and Bifurcation Analysis in a Class of Two-Neuron Networks with Resonant Bilinear Terms

Author(s) -

Changjin Xu,

Xiaofei He

Publication year - 2011

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 - 10.1155/2011/697630

Subject(s) - mathematics , center manifold , hopf bifurcation , zero (linguistics) , stability (learning theory) , pitchfork bifurcation , saddle node bifurcation , bilinear interpolation , mathematical analysis , bifurcation , stability theory , class (philosophy) , transcritical bifurcation , bifurcation diagram , nonlinear system , physics , linguistics , philosophy , statistics , quantum mechanics , machine learning , computer science , artificial intelligence

A class of two-neuron networks with resonant bilinear terms is considered. Thestability of the zero equilibrium and existence of Hopf bifurcation is studied. It is shown that the zeroequilibrium is locally asymptotically stable when the time delay is small enough, while change of stabilityof the zero equilibrium will cause a bifurcating periodic solution as the time delay passes through asequence of critical values. Some explicit formulae for determining the stability and the direction of theHopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normalform theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysisare carried out

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