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- Title
Chaos analysis of SD oscillator with two-frequency excitation.
- Authors
Peng, Ruyue; Li, Qunhong; Zhang, Wei
- Abstract
Homoclinic bifurcation in a class of SD oscillators under external quasi-periodic excitation with two frequencies is investigated. By using the Melnikov method, the Melnikov function of the system under two-frequency excitation is derived, and the threshold condition of chaos in the system is obtained. Based on the threshold condition, then a complete description of the bifurcation sets and the chaotic regions in the parameter space are presented. The parameters in the chaotic regions are selected for numerical simulation, and the chaotic motion is verified by calculating the largest Lyapunov exponent of the system. In addition, due to the geometric strong nonlinearity of the SD oscillator, there are infinitely many extreme points in the frequency-dependent function of the Melnikov function. The previous research on the frequency-dependent function of the Melnikov function is mainly focused on one or two extremes. In this work, the dynamical system with infinitely many extreme points in the frequency-dependent function is considered, and a conjecture of chaotic region under this condition is given.
- Subjects
CHAOS theory; DYNAMICAL systems; COMPUTER simulation; LYAPUNOV exponents; NONLINEAR oscillators; LOGICAL prediction
- Publication
Nonlinear Dynamics, 2024, Vol 112, Issue 9, p7649
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-024-09442-w