Dynamic Analysis And Control Of Complex Dynamical Systems With Hidden Attractors

Since Lorenz proposed the first chaos model in 1963,chaos has attracted attention in various fields and made great progress as an important research subject.In recent years,with the in-depth study of chaos phenomena in academia circle,the dynamic behavior change of chaos system and the control of chaos state have become an important content in the study of chaos.The dynamic analysis and control of chaotic systems has become a hotspot in the field of research because of its vital role in the development of secure communication and engineering technology.Compared with the low-dimensional system,the dynamic behavior of high-dimensional chaotic system is more complex,so from the perspective of application value,the study of high-dimensional system should be paid more attention to.In recent years,compared with the traditional attractor,hidden attractor,as a newly defined attractor,has attracted more attention due to its different dynamic behavior.The chaotic system with hidden attractors has special hidden properties,but due to its late discovery time,there are few researches on its dynamic behavior change and state control.Based on the study of chaos theory,this paper studies the dynamic behavior and control of chaotic systems with hidden attractors.The thesis includes the following aspects:1.The definition,basic characteristics and development history of chaotic systems are briefly described,and the research progress and related basic knowledge of chaos are introduced.2.Explore and analyze the hidden dynamic behavior and simulation problems of a class of two 3-D chaotic systems with different equilibrium points designed by changing parameters.The Matlab software was used to obtain the Lyapunov exponential map,chaotic attractor map,bifurcation map and Poincaré map of the two systems.The global dynamic behavior of the system was analyzed.With proper parameters,the existence of chaotic attractors and periodic attractors of the system and their coexistence are discussed by numerical simulation and other methods.3.The hidden dynamic behavior of a stable equilibrium chaotic system based on Stenflo system is studied.For example,the dynamical behaviors of attractor,such as dimension,dissipation,Lyapunov exponent and bifurcation,etc.The existence and coexistence of chaotic attractors and periodic attractors are discussed by numerical simulation.4.First,based on the state observation method,by designing an effective controller,the synchronization of the driving system and the response system of the chaotic system is achieved,and the results of numerical simulation verify the effectiveness of the method.Secondly,according to Helmholtz's theorem,the energy functions of the unbalance point,infinitely many equilibrium points,and systems with unique stable equilibrium points werecalculated,and the feedback control of the chaotic system was realized by designing effective control schemes and adjusting the corresponding feedback gain.It is found that the system can be controlled to the ideal periodic state,stable state,and chaotic state,and the effectiveness of the control scheme is verified by computer simulation.