期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 29, 期 1, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127419500020
关键词
Discontinuous system; random disordered periodic input; random Melnikov method; chaos
资金
- National Nature Science Foundation of China [11402139, 11572247]
- Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi [2016114]
In this paper, we extend the random Melnikov method from stochastic systems with a continuous vector field to discontinuous systems driven by a random disordered periodic input under the assumption that the unperturbed system is a piecewise Hamiltonian system. By measuring the distance of the perturbed stable and unstable manifolds, the nonsmooth random Melnikov process can be derived in detail, and then the mean square criterion for the onset of chaos is established in the statistical sense. It is shown that the threshold for the onset of chaos depends on the stochastic force and a scalar function of hypersurface. Finally, an example is given to analyze the chaotic dynamics using this extended approach, and discuss the effects of noise intensity on the dynamical behaviors of the system. The results indicate that the increase of the noise intensity will result in a chaotic motion of the discontinuous stochastic system and the changes of possible chaotic degree in the phase space. At the same time, the effects of noise intensity on chaos are further investigated through the system response including time history and phase portraits, Poincare maps and 0-1 test.
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