期刊
NONLINEAR DYNAMICS
卷 82, 期 3, 页码 1251-1258出版社
SPRINGER
DOI: 10.1007/s11071-015-2230-y
关键词
Chaotic attractor; Jerk system; Averaging theory; Non-hyperbolic equilibrium; Zero-Hopf bifurcation
资金
- Natural Science Foundation of China [11401543, 11290152, 11427802, 41230637]
- Natural Science Foundation of Hubei Province [2014CFB897]
- Beijing Postdoctoral Research Foundation [2015ZZ17]
- China Postdoctoral Science Foundation [2014M560028, 2015T80029]
- Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) [CUGL150419]
- Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)
This paper proposes a chaotic jerk system coexisting with only one non-hyperbolic equilibrium with one zero eigenvalue and a pair of complex conjugate eigenvalues. The system has no classical Hopf bifurcations and belongs to a newly category of chaotic systems. Based on the averaging theory, an analytic proof of the existence of zero-Hopf bifurcation is exhibited. Moreover, unstable periodic orbits from the zero-Hopf bifurcation are obtained. This approach may be useful to clarify chaotic attractors with non-hyperbolic equilibrium hidden behind complicated phenomena.
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