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Dynamic analysis of a 5D fractional-order hyperchaotic system

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  • Control Theory and Applications
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Abstract

In this paper, the fractional-order 5D hyperchaotic system is proposed based on the hyperchaotic Lorenz system. Fractional-order chaotic systems are often three- or four-dimensional. There are few results about high dimension fractional-order systems. For this 5D hyperchaotic system, the stability of equilibrium points is analyzed by means of the stability theory of fractional systems. Then the fractional bifurcation is investigated. It is found that the system admits bifurcations with varying fractional-order and parameters, respectively. Under different bifurcation parameters, some conditions ensuring the bifurcations are presented. Finally, numerical simulations are presented to confirm the given analytical results.

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Authors and Affiliations

  1. Department of Mathematics, School of Anhui University, Hefei, 230601, China

    Shan Wang & Ranchao Wu

Authors
  1. Shan Wang
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  2. Ranchao Wu
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Corresponding author

Correspondence to Ranchao Wu.

Additional information

Recommended by Associate Editor Ho Jae Lee under the direction of Editor Yoshito Ohta. This work was supported by the National Science Foundation of China (No. 11571016, 61403115), the Natural Science Foundation of Anhui Province (No. 11040606M12) and the 211 project of Anhui University (No. KJJQ1102, KJTD002B).

Shan Wang was born in Hubei, China in 1990. She is received the B.S. degree at the Department of Mathematics from Anhui University in 2016. Her research interests include dynamical system theory, bifurcation, control, chaos and their applications.

Ranchao Wu born in Anhui, China in 1971. He received his Ph.D. degree in Mathematics from Nanjing University, in 2003 and 2006. He is currently a Professor in the Anhui University, Hefei, China. His research interests include dynamical system theory, bifurcation, control,chaos and their applications.

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Wang, S., Wu, R. Dynamic analysis of a 5D fractional-order hyperchaotic system. Int. J. Control Autom. Syst. 15, 1003–1010 (2017). https://doi.org/10.1007/s12555-015-0167-z

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  • DOI: https://doi.org/10.1007/s12555-015-0167-z

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