TOPOLOGICAL HORSESHOE IN A FRACTIONAL-ORDER QI FOUR-WING CHAOTIC SYSTEM

Yanling Guo; Guoyuan Qi

doi:10.11948/2015015

2015 Volume 5 Issue 2

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Yanling Guo, Guoyuan Qi. TOPOLOGICAL HORSESHOE IN A FRACTIONAL-ORDER QI FOUR-WING CHAOTIC SYSTEM[J]. Journal of Applied Analysis & Computation, 2015, 5(2): 168-176. doi: 10.11948/2015015

Citation:

Yanling Guo, Guoyuan Qi. TOPOLOGICAL HORSESHOE IN A FRACTIONAL-ORDER QI FOUR-WING CHAOTIC SYSTEM[J]. Journal of Applied Analysis & Computation, 2015, 5(2): 168-176. doi: 10.11948/2015015

TOPOLOGICAL HORSESHOE IN A FRACTIONAL-ORDER QI FOUR-WING CHAOTIC SYSTEM

Yanling Guo¹,
Guoyuan Qi^2,3

1 F'SATIE, Department of Electrical Engineering, Tshwane University of Technology, Pretoria, 0001, South Africa;
2 College of Electrical Engineering and Automation, Tianjin Polytechnic University, Tianjin 300384, P R China;
3 Department of Electrical and Mining Engineering, University of South Africa, South Africa, 1710

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Abstract

Abstract

A fractional-order Qi four-wing chaotic system is present based on the Grünwald-Letnikov definition. The existence of topological horseshoe in a fractional chaotic system is analyzed by utilizing topological horseshoe theory. A Poincaré section is properly chosen to obtain the Poincaré map which is proved to be semi-conjugate to a 2-shift map, implying that the fractional-order Qi four-wing chaotic system exhibits chaos.
- Fractional-order system /
- topological horseshoe /
- Poincaré map /
- topologcal entropy /
- Qi four-wing chaotic system
MSC: 37B40;65P20

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References

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