Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation | Zendy

Ming Liu | Zendy; Xiaofeng Xu | Zendy

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Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation

Author(s) -

Ming Liu,

Xiaofeng Xu

Publication year - 2013

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 - 10.1155/2013/367589

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

The dynamics of a 2-dimensional neural network model in neutral form are investigated. We prove that a sequence of Hopf bifurcations occurs at the origin as the delay increases. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are determined by using normal form method and center manifold theory. Global existence of periodic solutions is established using a global Hopf bifurcation result of Krawcewicz et al. Finally, some numerical simulations are carried out to support the analytic results

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