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Double Hopf bifurcation in a four-neuron delayed system with inertial terms

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Abstract

In this paper, a four-neuron delayed system with inertial terms is considered. By studying the distribution of the eigenvalues of the associated characteristic equation, we derive the critical values where double Hopf bifurcation occurs. Then by employing the perturbation-incremental scheme for the system, bifurcation diagrams are obtained. Furthermore, we carry out bifurcation analysis showing that there exist a stable fixed point, two stable periodic solutions, co-existence of a pair of stable periodic solutions and quasi-periodic motion in the neighborhood of the double Hopf critical point. We also find some interesting phenomena that the dynamical period switching occurs in some delayed regions. Finally, some numerical simulations are performed to support the theoretical analysis.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11202068, 11272236, 61203050 and 11302072) and University Key Teacher Foundation for Youths of Henan Province (Grant No. 2014GGJS-076).

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Authors and Affiliations

  1. School of Mathematics and Information Science, He’nan University of Economics and Law, Zhengzhou, 450002, China

    JuHong Ge

  2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Jian Xu

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  1. JuHong Ge
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  2. Jian Xu
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Correspondence to JuHong Ge.

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Ge, J., Xu, J. Double Hopf bifurcation in a four-neuron delayed system with inertial terms. Nonlinear Dyn 82, 1969–1978 (2015). https://doi.org/10.1007/s11071-015-2291-y

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  • DOI: https://doi.org/10.1007/s11071-015-2291-y

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