Circuitry Implementation And Theoretical Study On High Dimensional And Delayed Chaotic System

Over the last two decades, chaos has gradually moved from simply being a scientific curiosity to a promising subject with practical significance and applications. Since the first paradigm of the well-known Lorenz system,chaotic systems have been considered as a rich mechanism for signal design and generation and they have potential applications to data encryption, secure communications and signal processing. It has been noticed that, purposefully generating or enhancing chaos can be a key issue in many technological and engineering applications.This thesis addresses three important issues involved in chaotic systems: mechanism of generating chaos in nonlinear circuits, construction of chaos generators and adaptive chaos synchronization. Specifically, the main contributions of this thesis are presented as follows.The preliminary knowledge involved in this thesis, including the definitions of chaos, the characteristics, the criterions and rules of chaos, and chaos phenomena in nonlinear circuits, are introduced.It is well known that chaos can neither occur in first- or second-order autonomous continuous-time system, nor in a first-order non-autonomous continuous-time system. Chaos has been found in three-order autonomous continuous-time system. Several typical chaos systems and circuitry implementation are analyzed in detail.Aiming at low-dimensional systems having low security to be easily captured, enhancement of chaos in nonlinear system should be considered. An electronic analog of a new four-dimensional continuous autonomous chaotic system is described in detail. The proposed circuit may be used as chaos generator and has potential applications to communications and signal processing.However, with the increase of dimension, the system become more complex and hard to implement with electronic circuitry. Fortunately, it is found that simple neural networks with time delays can exhibit chaotic dynamical behavior. Chaotic phenomena for delayed neural networks consisting of two or three non-linear neurons have also been found. In this thesis, the local stability and existence of Hopf bifurcation, the loss of stability of a limit circle and the numerical transition to chaos of delayed differential equations are studied.Based on the above work, a circuitry implementation of chaotic Liao's delayed...