Dynamic Analysis Of Several Classes Of High Dimensional Autonomous And Non-autonomous Nonlinear Systems

This paper mainly studies bifurcation and chaotic behaviors of three kinds of nonlinear dynamical systems.Nonlinear dynamical characteristics for a class of magnetorheological damper system are investigated in the first model.The dynamical behavior of the system is analyzed by using bifurcation theory.The results of the theoretical analysis are verified by numerical simulations.Stability and bifurcation analysis of a new four-dimensional autonomous system are studied with the aid of center manifold and normal form theory in the second model.The critical bifurcation lines leading to incipient and secondary bifurcations are obtained.Possible bifurcations leading to 2-D tori are also investigated.Numerical simulations confirm the analytical results.Utilized both analytical and numerical methods,subharmonic bifurcations and chaotic motions of a carbon nanotube supported by a Winkler and Pasternak foundation are investigated in the third model.The threshold for chaotic motions together with the critical curves separating the chaotic and non-chaotic regions is obtained.It is proved that the system can undergo chaotic motions through infinite subharmonic bifurcations.