Dynamic Behavior Analysis Of A Class Of State-dependent Switched Nonlinear Systems

With the development of science and technology and the progress of research methods,the complicated nonlinear switched systems are attracting more and more attention because of its wide application background. Nonlinear switched system related to state is an important part of nonlinear switched systems, which has great application prospects. Through the numerical simulation, using the theory of nonlinear dynamics and switched system,oscillating characteristic and bifurcation behavior of the system are analyzed, and the influence of breaking time due to switching in practical application on the stability of the switched system is considered.Furthermore,the bifurcation behavior of switched system alternated between two subsystems by two different critical states considering breaking time due to switching is analyzed. The research work of this paper mainly has the following several aspects :Firstly,the complicated behaviors as well as the mechanism of the vector field of switched system alternated between two subsystems by two different critical states are investigated in this paper. Upon employing the typical generalized BVP oscillator as an example, by introducing bilateral switch, the nonlinear dynamical model alternated between two subsystems related two states is established, the different movement forms as well as the dynamical evolution of which caused by switches are explored in details. Based on the Poincare theory of nonlinear system, the computational equation of Lyapunov exponents of switched system is derived. Combined with the bifurcation analysis of subsystems, different oscillations of the system are discussed, upon which the nonlinear behaviors such as sudden changes of period in periodic oscillations and the route to chaos with period-doubling bifurcations as well as the related essence are presented.Secondly,before analyzing the effects of breaking time on switched system alternated between two subsystems by two different critical states,the one critical state condition has been analyzed.Upon employing the typical generalized BVP oscillator as an example, by introducing unilateral switch, the nonlinear dynamical modelrelated to the state and breaking time is established, the different movement forms as well as the dynamical evolution of which caused by switches are explored in details.Based on the breaking time, the phase diagram,time history and bifurcation diagram are analyzed.Combined with the bifurcation analysis of subsystems, different oscillations of the system are discussed, upon which the nonlinear behaviors such as special periodic oscillations and the transformation process between chaos and periodic solution are presented.At last,on the base of the last two researches, the effects of breaking time on switched system alternated between two subsystems by two different critical states has been analyzed. Upon employing the extended BVP switched oscillator as an example,through the comparison of the oscillating characteristic of switched system between before and after considering the breaking time,we found the breaking time has a great influence on the oscillating characteristic of switched system.Furthermore,by analyzing the bifurcation diagrams of switched system with different breaking time,we found the breaking time has different influence on the different type of oscillation behavior.Also,a special period-doubling bifurcation has been found by analyzing the bifurcation diagram.