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Dynamical analysis in a 4D hyperchaotic system

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Abstract

Inspirited by Li and Jin (Nonlinear Dyn. 67:2857–2864 2012), this paper investigates the Hopf bifurcation of a four-dimensional hyperchaotic system with only one equilibrium. A detailed set of conditions are derived, which guarantee the existence of the Hopf bifurcation. Furthermore, the standard normal form theory is applied to determine the direction and type of the Hopf bifurcation, and the approximate expressions of bifurcating periodic solutions and their periods. In addition, numerical simulations are used to justify theoretical results.

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Authors and Affiliations

  1. School of Science, Linyi University, Linyi, 276005, Shandong, China

    Hongwei Li

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  1. Hongwei Li
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Correspondence to Hongwei Li.

Additional information

This research was partially supported by the Nature Science Foundation of Shandong Province (ZR2012AL04).

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Li, H. Dynamical analysis in a 4D hyperchaotic system. Nonlinear Dyn 70, 1327–1334 (2012). https://doi.org/10.1007/s11071-012-0536-6

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  • DOI: https://doi.org/10.1007/s11071-012-0536-6

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