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Stability and Bifurcation of a Class of Discrete-Time Cohen–Grossberg Neural Networks with Discrete Delays

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Abstract

A class of discrete-time Cohen–Grossberg neural networks with discrete delays and ring-architecture are investigated in this paper. By analyzing the corresponding characteristic equations, the existence of Neimark–Sacker bifurcations at the origin are obtained. By applying the normal form theory and the center manifold theorem, the direction of the Neimark–Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Sufficient conditions to guarantee the global stability of the null solution of such networks are established by using suitable Lyapunov function and the properties of M-matrix. Numerical simulations are given to illustrate the obtained results.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, China

    Qiming Liu

  2. Department of Information Engineering, Shijiazhuang Mechanical Engineering College, Shijiazhuang, 050003, China

    Sumin Yang

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  1. Qiming Liu
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  2. Sumin Yang
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Correspondence to Qiming Liu.

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Liu, Q., Yang, S. Stability and Bifurcation of a Class of Discrete-Time Cohen–Grossberg Neural Networks with Discrete Delays. Neural Process Lett 40, 289–300 (2014). https://doi.org/10.1007/s11063-013-9329-2

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  • DOI: https://doi.org/10.1007/s11063-013-9329-2

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