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Rapid fluctuation for topological dynamical systems |
Yu HUANG1( ), Yi ZHOU2 |
| 1. Department of Mathematics, Zhongshan (Sun Yat-sen) University, Guangzhou 510275, China; 2. Department of Biomedical Engineering, Zhongshan School of Medicine, Zhongshan (Sun Yat-sen) University, Guangzhou 510080, China |
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Abstract In this paper, we introduce a new notion called rapid ?uctuation to characterize the complexity of a general topological dynamical system. As a continuation of the former work [Huang, Chen, Ma, J. Math. Anal. Appl., 2006, 323: 228-252], here we prove that a Lipschitz dynamical system de?ned on a compact metric space has a rapid ?uctuation if it has either a quasi shift invariant set or a topological horseshoe. As an application, the rapid ?uctuation of a discrete predator-prey model is considered.
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| Keywords
Rapid ?uctuation
quasi-shift invariant set
topological horseshoe
Hausdorff dimension
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Corresponding Author(s):
HUANG Yu,Email:stshyu@mail.sysu.edu.cn
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Issue Date: 05 September 2009
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