Complex Dynamics Analysis And Transient Behavior Study Of Dissipative Chaotic Systems

For more than half a century,chaos theory has made great development in many disciplines,especially in image encryption,neural network and communication security.The research on chaotic system with rich dynamic characteristics has become an important research topic of nonlinear system.Transient can usually be found in some dynamic systems.The transient behavior is the time evolution before asymptotic dynamics.In the observation,modeling,prediction and control of nonlinear systems,transient behavior may play a more important role than the asymptotic state of nonlinear systems.It is very important for nonlinear dynamic systems in physics,chemistry,biology,engineering,economics and even social sciences.Therefore,the study of transient behavior is a key issue worthy of attention.This thesis mainly studies the improved Sprott-C system,four-dimensional smooth chaotic system and classical Lorenz chaotic system.It mainly studies the system modeling,basic dynamic behavior,transient behavior and weak signal detection.The specific research work of this thesis is summarized as follow:(1)Firstly,a dissipative chaotic system with variable divergence is proposed based on Sprott-C system.Through the analysis of Hamilton energy,the chaotic mechanism of the system is revealed.The boundary,equilibria and Hopf bifurcation of the system are studied by using Lagrange multiplier method and Cartan formula.Two new indexes are proposed to analyze the variable divergence.Then the multistability and hidden attractors of the system are analyzed.Finally,the transient behavior of the system is analyzed by using the time series simplification method.(2)Based on the dissipative chaotic system with variable divergence proposed in this thesis,a four-dimensional smooth chaotic system is proposed.The rich dynamic behavior of the system is analyzed.Under different parameters,the system can be divided into three different regions corresponding to three different chaotic attractors.The transient behavior of the third region of the system is analyzed by using the time series simplification method,the causes of transient chaos are revealed,and the predictability of the transient duration of the transient quasi-periodic is found.Finally,the influence of the position and eigenvalue of the stable equilibrium point on the boundary crisis is analyzed by using the control variable method.(3)In order to verify the universality of the transient quasi-period proposed in this thesis,the transient quasi-period in the classical Lorenz system is analyzed.The influence of initial point on transient quasi-period under different termination conditions is analyzed by using basin diagram,and the predictability of quasi-period amplitude and transient quasi-period life is found.By analyzing the attractor trajectory,the necessary conditions for the generation of transient quasi-period are revealed.Then the noise immunity of weak signal detection system is analyzed.Finally,the relationship between transient quasi-periodic duration and driving signal amplitude under the influence of Gaussian noise with mean value of 0 is analyzed.It is found that the transient quasi-periodic duration can be used to predict the signal amplitude to be measured.