Research On The Model Analysis And Analog Circuit Of The Chaotic And Hyperchaotic Systems

Chaos is one of the modes of motion in nonlinear system, and the phenomenon of chaos is ubiquitous in nature. Since the American meteorologist Lorenz found the fist chaotic attractor in the deterministic dissipative system in 1963, the study on chaotic attractor has attracted more and more interests. Recently, chaos theory and its application have been developed rapidly. Chaotic systems are complex nonlinear systems. To deeply study the complex chaotic systems, one should not only analyze them theoretically, such as dynamical behavior analysis and proof for the existence of chaos, but also investigate the characteristics of them by the physical implementation, namely the analog circuits.With respect to theoretical analysis and circuit implementation of chaotic systems, the innovation work in the thesis is summarized as follows.This thesis firstly does numerical simulation study on a four-wing chaotic systems reported by Chen Zengqiang et al. Based on Poincare map, by using the topological horseshoe theory presented by Yang et al. and computer-assisted proof, it is verified that topological horseshoes exist in the system, and thus the existence of chaos is proved theoretically. An analog hardware circuit is also made for the four-wing chaotic system, and the results of circuit experiment observed by oscillation are well consistent with those of simulation. Furthermore, the characteristics of the four-wing chaotic system are verified physically. In addition, it is also proved that topological horseshoe exists in a Qi four-wing chaotic system by utilizing the topological horseshoe theorem.In recent years, the generation and the application of hyper-chaos have become a hot topic of chaos. The thesis also focuses on the hardware implementation of the presented hyperchaotic systems. Based on deeply analyzing those hyperchaotic systems, a new hyperchaotic system which possesses a larger parameter range and two bigger positive Lyapunov exponents is also presented. It is implemented it by an analog circuit.Lii system is a transition system between the Lorenz system and the Chen system in generalized Lorenz system. The thesis also presents a novel hyper-chaotic Lii system with only one equilibrium. The local bifurcation is analyzed by virtue of center manifold theory. An analog circuit is designed to study the hyperchaotic attractor.