Journal
NONLINEAR DYNAMICS
Volume 83, Issue 1-2, Pages 1069-1078Publisher
SPRINGER
DOI: 10.1007/s11071-015-2388-3
Keywords
Index theory; Topological structure; Multi-wing chaotic attractor; Lyapunov exponents
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Funding
- Natural Science Foundation of China [61174094, 11202148, 61403274]
- Tianjin Natural Science Foundation [14JCYBJC18700]
- Application Base and Frontier Technology Research Project of Tianjin of China [13JCQNJC03600]
- Shandong Natural Science Foundation [ZR2012FM034]
- China/South Africa Research Cooperation Programme [78673, CS06-L02]
- South African National Research Foundation [81705]
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This paper proposed a new method for exploring three-dimensional chaotic attractors with complicated topological structure. Based on the index theory, the theoretical foundation of the new method is explained clearly and concisely, and the feasibility of this method is progressively illustrated by a multi-wing three-dimensional chaotic attractor derived from a two-dimensional continuous autonomous dynamical system with thirteen equilibrium points. Moreover, the experimental results are also discussed. To validate the generalization ability of the proposed method, another two chaotic systems are constructed based on the proposed method. The numerical results show the effectiveness of the proposed method.
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