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Chaotic motion of Van der Pol–Mathieu–Duffing system under bounded noise parametric excitation

Authors
Journal
Journal of Sound and Vibration
0022-460X
Publisher
Elsevier
Publication Date
Volume
309
Identifiers
DOI: 10.1016/j.jsv.2007.05.027
Disciplines
  • Mathematics

Abstract

Abstract The chaotic behavior of Van der Pol–Mathieu–Duffing oscillator under bounded noise is investigated. By using random Melnikov technique, a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system. The results show that the threshold of bounded noise amplitude for the onset of chaos in this system increases as the intensity of the noise in frequency increases, which is further verified by the maximal Lyapunov exponents of the system. The effect of bounded noise on Poincaré map is also investigated, in addition the numerical simulation of the maximal Lyapunov exponents.

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