Homoclinic Bifurcation and Chaos in a Noise-Induced Φ6 Potential
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-13
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The present paper focuses on the noise-induced chaos in a Φ6 oscillator with nonlinear damping.
Based on the stochastic Melnikov approach, simple zero points of the stochastic Melnikov integral theoretically mean the necessary condition causing noise-induced chaotic responses in the system.
To quantify the noise-induced chaos, the Poincare maps and fractal basin boundaries are constructed to show how the system's motions change from a periodic way to chaos or from random motions to random chaos as the amplitude of the noise increases.
Three cases are considered in simulating the system; that is, the system is excited only by the harmonic excitation, by both the harmonic and the Gaussian white noise excitations, or by both the bounded noise and the Gaussian white noise excitations.
The results show that chaotic attractor is diffused by the noises.
The larger the noise intensity is, the more diffused attractor it results in.
And the boundary of the safe basin can also be fractal if the system is excited by the noises.
The erosion of the safe basin can be aggravated when the frequency disturbing parameter of the bounded noise or the amplitude of the Gaussian white noise excitation is increased.
American Psychological Association (APA)
Ge, Gen& Zhu, Zhiwen& Xu, Jia. 2013. Homoclinic Bifurcation and Chaos in a Noise-Induced Φ6 Potential. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-1031798
Modern Language Association (MLA)
Ge, Gen…[et al.]. Homoclinic Bifurcation and Chaos in a Noise-Induced Φ6 Potential. Mathematical Problems in Engineering No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-1031798
American Medical Association (AMA)
Ge, Gen& Zhu, Zhiwen& Xu, Jia. Homoclinic Bifurcation and Chaos in a Noise-Induced Φ6 Potential. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-1031798
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1031798