The effects of constant excitation on the recently proposed smooth-and-discontinuous(SD)oscillator are investigated,which may lead to the variation of equilibrium and the property of phase portrait.By solving a quarti...The effects of constant excitation on the recently proposed smooth-and-discontinuous(SD)oscillator are investigated,which may lead to the variation of equilibrium and the property of phase portrait.By solving a quartic algebraic equation,the transition set and bifurcation for SD oscillator under constant excitation(CSD)are presented,while the number of equilibria depends on the values of the smoothness parameter and the constant excitation.Complicated structures of Kolmogorov–Arnold–Moser(KAM)structures on the Poincarésection are depicted for the driven system without dissipation.Chaotic behaviour is also demonstrated numerically for the system perturbed by both viscous-damping and external excitation.The results show that CSD is an unsymmetrical system that displays different dynamical behaviours from an SD oscillator and will enrich the range of the SD oscillator in research and application.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11002093 and 11172183the Science and Technology Plan Project of Hebei Science and Technology Department(No 11215643).
文摘The effects of constant excitation on the recently proposed smooth-and-discontinuous(SD)oscillator are investigated,which may lead to the variation of equilibrium and the property of phase portrait.By solving a quartic algebraic equation,the transition set and bifurcation for SD oscillator under constant excitation(CSD)are presented,while the number of equilibria depends on the values of the smoothness parameter and the constant excitation.Complicated structures of Kolmogorov–Arnold–Moser(KAM)structures on the Poincarésection are depicted for the driven system without dissipation.Chaotic behaviour is also demonstrated numerically for the system perturbed by both viscous-damping and external excitation.The results show that CSD is an unsymmetrical system that displays different dynamical behaviours from an SD oscillator and will enrich the range of the SD oscillator in research and application.