Regular and chaotic oscillations in a modified Rayleigh-Liénard system under parametric excitation. (English) Zbl 1477.70041

Summary: In this paper, the regular and chaotic oscillations in a modified Rayleigh-Liénard system under parametric excitation are studied. Two subharmonic resonant states are generated using the multiple time scales method and the effects of the system parameters on the frequency-response curves are investigated. Bifurcation structures and transitions to chaos for the first subharmonic resonant state are numerically investigated via the fourth-order Runge-Kutta integration algorithm, and symmetry-breaking, period-doubling, period-windows, intermittency and antimonotonicity phenomena are obtained. The influences of the nonlinear damping coefficients, cubic nonlinearity coefficient and small dimensionless coefficient on the bifurcation sequences are also investigated. As results, it is found that the nonlinear damping coefficients and cubic nonlinearity coefficient can be used to control the presence of chaos in the system while decreasing of the small dimensionless parameter removes chaos from the system.


70K55 Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K40 Forced motions for nonlinear problems in mechanics
70K50 Bifurcations and instability for nonlinear problems in mechanics
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
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