Dynamic Analysis And Application Of Several Kinds Of Nonlinear Systems

The research of nonlinear systems has always been the focus of the scientific community.However,due to the late start,most of the current researches are directed to chaotic systems with integer order and no time delay.The research on fractional systems and time-delay systems countable.The research of linear science has been quite mature,and the significance of applying the research results of nonlinear systems to life production is even more significant.In this paper,three nonlinear systems of Lorenz system,Chen system and Rucklidge system are studied,and the complexity characteristics of arbitrary order and the influence of time-delay factors under integer order on system stability are analyzed.According to the spectral entropy complexity and C0 complexity calculation method,the system complexity change map under single parameter and multi-parameter is drawn.The characteristic root step method and Hopf bifurcation theory are used to analyze the typical systems of Lorenz system,Chen system and Rucklidge system.Dynamics under time-delay disturbances.According to the Routh-Hurwitz criterion,the stability of each equilibrium point is determined sequentially,and the stability conditions are given.The stability is verified by the Lyapunov exponent diagram.The Hopf bifurcation is analyzed for the unstable equilibrium point.The bifurcation feature of the system is calculated according to the eigenroot step method and the Hopf bifurcation theory.The Hopf bifurcation type and direction are judged,and the Hopf bifurcation condition is obtained.The matlab value is obtained.The simulation verifies the calculation result.According to the analysis results,the Hopf bifurcation control theory is designed with reference to the existing Hopf bifurcation control theory without time-delay system.The Hopf bifurcation delay and early control are designed to study the system,which provides a reference for the subsequent study of singledelay and multi-time-delay systems.In order to strengthen the practical application speed of this paper,according to the nonlinear analog circuit theory,select electrical components and build nonlinear circuits.The distribution of the system’s eigenvalues is calculated,and the distribution results are used to calculate the time-delay parameters of Hopf bifurcation.Using the calculation results,the Chen robot with the parameter item is added to the navigation path of the wireless robot,and the path map is drawn.The actual operation results show that the time-delay parameter determined by this method can increase the robot’s path coverage to more than 80%.