期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 29, 期 12, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127419501669
关键词
Chaos; multistability; equilibria; hidden attractors; coexisting attractors; center manifold theory
资金
- National Natural Science Foundation of China [11671149]
- Natural Science Foundation of Guangdong Province [2017A030312006]
Intuitively, a finite-dimensional autonomous system of ordinary differential equations can only generate finitely many chaotic attractors. Amazingly, however, this paper finds a three-dimensional autonomous dynamical system that can generate infinitely many chaotic attractors. Specifically, this system can generate infinitely many coexisting chaotic attractors and infinitely many coexisting periodic attractors in the following three cases: (i) no equilibria, (ii) only infinitely many nonhyperbolic double-zero equilibria, and (iii) both infinitely many hyperbolic saddles and nonhyperbolic pure-imaginary equilibria. By analyzing the stability of double-zero and pure-imaginary equilibria, it is shown that the classic Shil'nikov criteria fail in verifying the existence of chaos in the above three cases.
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