Exploration Of Conservative Chaos And Study On Hidden Dynamics In Dynamical Systems

Chaos as a very common motion has important application value in nonlinear dynamical systems,and can explain the complex nonlinear phenomena generated by physical systems.At present,dynamic analysis of chaotic systems,time series analysis of chaotic signals,and streaming media encryption technology based on chaotic signals are the chaotic research hotspots,but these studies mainly focu on dissipative chaos,and few studies on conservative chaos.Recent years,the construction,theoretical analysis and application of conservative chaos have been studied and further enrich the chaos theory.This thesis focuses on constructing a three-dimensional conservative system with complex topological structures that can generate multicluster conservative chaotic flows and invariant toris.In addition,the hidden dynamic characteristics of a Lorenz-like system are also studied.Specific research contents include:First,the Sprott-A system is decomposed and transformed into the matrix differential equation form based on the generalized Hamiltonian system theory;A modified Sprott-A system,a generalized Sprott-A system and a non-Hamiltonian system are obtained by configuring the skew-symmetric matrix or Hamiltonian of the Sprott-A system.The dynamic characteristics of these systems are investigated from both theoretical and numerical analysis,the results suggest these systems can generate conservative chaos and invariant toris for different initial conditions or parameters.Second,a general method for constructing volume-conservative systems is proposed based on the generalized Hamiltonian system theory and a non-Hamiltonian system model is proposed to verify the effectiveness of this method.This thesis proposes three subsystems and are analyzed from the aspects of stability of equilibrium points,topological structure of chaotic flow,and energy analysis.Numerical results show that the system constructed by the proposed method can generate conservative chaotic flows and invariant toris with different topological structures.Third,a Lorenz-like system are studied from equilibrium point stability and dynamic characteristics under different parameters,which reflect this system exists rare hidden attractors and self-excited coexistent attractors.