The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and res...The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.展开更多
Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continu...Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continuous topologically transitive （in strongly successive way） functions fn ： X →X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney＇s definition is lost on the limit function.展开更多
We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto's theorem is first proved, and the bifurcations of periodic points ...We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto's theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10872141, 11072168)the National Hi-Tech Research and Development Program of China ("863" Project) (Grant No. 2008AA042406)
文摘The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.
基金CSIR ( project no. F.NO. 8/3(45)/2005-EMR-I)for providing financial support to carry out the research work
文摘Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f ： X →X of a sequence of continuous topologically transitive （in strongly successive way） functions fn ： X →X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney＇s definition is lost on the limit function.
基金Supported by Chinese Academy Sciences (KZCX2-SW-118).
文摘We consider the dynamics of a two-dimensional map proposed by Maynard Smith as a population model. The existence of chaos in the sense of Marotto's theorem is first proved, and the bifurcations of periodic points are studied by analytic methods. The numerical simulations not only show the consistence with the theoretical analysis but also exhibi the complex dynamical behaviors.
