期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 18, 期 5, 页码 1393-1414出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127408021063
关键词
chaos; bifurcation; Lyapunov exponent; Lorenz system; Chen system; Lu system
资金
- National Natural Science Foundation of China [10461002]
- City University of Hong Kong [7002134]
- Natural Science Foundation of Guangdong Province of China [05300162]
This paper reports the finding of a chaotic system with one saddle and two stable node-foci in a simple three-dimensional (3D) autonomous system. The system connects the original Lorenz system and the original Chen system and represents a transition from one to the other. The algebraical form of the chaotic attractor is very similar to the Lorenz-type systems but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact that the chaotic system has a chaotic attractor, one saddle and two stable node-foci. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations.
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