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Entropy 2015, 17(8), 5561-5579;

A New Chaotic System with Positive Topological Entropy

Department of Physics and Electronics, Binzhou University, Binzhou 256600, China
College of Computer and Control Engineering, Nankai University, Tianjin 300071, China
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
Received: 26 April 2015 / Revised: 25 July 2015 / Accepted: 29 July 2015 / Published: 3 August 2015
(This article belongs to the Section Complexity)
View Full-Text   |   Download PDF [12184 KB, uploaded 3 August 2015]   |  


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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wang, Z.; Ma, J.; Chen, Z.; Zhang, Q. A New Chaotic System with Positive Topological Entropy. Entropy 2015, 17, 5561-5579.

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