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Zero-Hopf bifurcation analysis in an inertial two-neural system with delayed Crespi function

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Abstract

In this paper, we study a four-dimensional inertial two-nervous system with delay. By analyzing the distribution of eigenvalues, the critical value of zero-Hopf bifurcation is obtained. Complex dynamic behaviors are considered when two parameters change simultaneously. Pitchfork and Hopf bifurcation critical lines at near the zero-Hopf point are obtained by using the central manifold reduction and the normal form theory. The bifurcation diagram is given, and the results of period-doubling bifurcation into chaotic region in the inertial two-neural system with delayed Crespi function are shown.

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Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, P.R. China

    Yingying Li, Li Xiao & Zhouchao Wei

  2. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, P.R. China

    Wei Zhang

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  1. Yingying Li
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  2. Li Xiao
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  3. Zhouchao Wei
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  4. Wei Zhang
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Correspondence to Zhouchao Wei.

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Li, Y., Xiao, L., Wei, Z. et al. Zero-Hopf bifurcation analysis in an inertial two-neural system with delayed Crespi function. Eur. Phys. J. Spec. Top. 229, 953–962 (2020). https://doi.org/10.1140/epjst/e2020-900159-8

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