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Open AccessArticle

A New Chaotic System with Positive Topological Entropy

1
Department of Physics and Electronics, Binzhou University, Binzhou 256600, China
2
College of Computer and Control Engineering, Nankai University, Tianjin 300071, China
3
College of Science, Civil Aviation University of China, Tianjin 300300, China
*
Author to whom correspondence should be addressed.
Academic Editors: Guanrong Chen, C.K. Michael Tse, Mustak E. Yalcin, Hai Yu and Mattia Frasca
Entropy 2015, 17(8), 5561-5579; https://doi.org/10.3390/e17085561
Received: 26 April 2015 / Revised: 25 July 2015 / Accepted: 29 July 2015 / Published: 3 August 2015
(This article belongs to the Section Complexity)
This paper introduces a new simple system with a butterfly chaotic attractor. This system has rich and complex dynamics. With some typical parameters, its Lyapunov dimension is greater than other known three dimensional chaotic systems. It exhibits chaotic behavior over a large range of parameters, and the divergence of flow of this system is not a constant. The dynamics of this new system are analyzed via Lyapunov exponent spectrum, bifurcation diagrams, phase portraits and the Poincaré map. The compound structures of this new system are also analyzed. By means of topological horseshoe theory and numerical computation, the Poincaré map defined for the system is proved to be semi-conjugate to 3-shift map, and thus the system has positive topological entropy. View Full-Text
Keywords: chaos; compound structures; topological horseshoe; topological entropy chaos; compound structures; topological horseshoe; topological entropy
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MDPI and ACS Style

Wang, Z.; Ma, J.; Chen, Z.; Zhang, Q. A New Chaotic System with Positive Topological Entropy. Entropy 2015, 17, 5561-5579. https://doi.org/10.3390/e17085561

AMA Style

Wang Z, Ma J, Chen Z, Zhang Q. A New Chaotic System with Positive Topological Entropy. Entropy. 2015; 17(8):5561-5579. https://doi.org/10.3390/e17085561

Chicago/Turabian Style

Wang, Zhonglin; Ma, Jian; Chen, Zengqiang; Zhang, Qing. 2015. "A New Chaotic System with Positive Topological Entropy" Entropy 17, no. 8: 5561-5579. https://doi.org/10.3390/e17085561

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