Study On Some Synchronization Control Methods Of Chaotic Systems And The Applications

Chaotic systems are well known for their very complex nonlinear systems, and have been intensively studied in various fields such as biology, physics, chemistry, engineering and information. Since it has the characteristics of sensitivity to initial values, high randomicity and certainty to nonlinear equations, chaos attracts great attentions from investigators. Chaotic synchronization is an important research aspect in chaotic science. Since 1990, chaos synchronization has achieved rapid development, and there have lots of remarkable results reported about it.Based on control theories of nonlinear systems, this dissertation studies the synchronization control methods and applications of integral-order and fractional-order chaotic systems. The main contributions are listed as follows:(1) A new complex fast synchronization control method is proposed for chaotic systems.Synthesizing the advantages of drive-response synchronization and coupled synchronization methods, a new complex fast synchronization control method is proposed. The simulation researches of Lorenz chaotic system and Liu chaotic system show that this method obviously shortens the synchronization time of chaotic systems and improves the synchronization dynamic performance.(2) Single-driving synchroniaiton and state observation synchronition methods are proposed for a new MLS chaotic system.Firstly, based on the analysis of the chaotic characteristic for a new four-dimensional piecewise MLS chaotic system, a single-driving synchronization method is proposed. This method has simple structures and is esay to be realized. Secondly, the state observation synchronization method is proposed. This method owns various formats in controllers, which provides multiforms schemes for project applications.(3) Q-S synchronization and generalized projective synchronization methods are proposed for different structure chaotic systems.Firstly, the Backstepping synchronization method is proposed for hyperchaotic Liu chaotic system and Genesio chaotic system. In this method single-driving and multi-driving synchronization controllers are designed to realize Q-S synchronization format, which simplifies the structures of controllers. Secondly, the improved generalized projective synchronization method is proposed for hyperchaotic Wang system and hyperchaotic Liu system. This method is agile to change the mutative parameters in synchronization controllers, which can adjust the synchronization speed and formats for chaotic systems.(4) The complete synchronization and generalized projective synchronization methods are proposed for a new fractional-order LS chaotic system.Firstly, after analyzing the dynamical characteristic for a new fractional-order LS chaotic system, the complete synchronization control method is proposed for this fractional-order system based on Laplace transform theory. The structures of controllers are simple and the effect of synchronization is satisfied. Secondly, the generalized projective synchronization control method is proposed for fractional-order LS system applying the stability theory of linear fractional-order system. The designs of controllers use less information of original drive system, so it is easy to be realized.(5) The chaotic applications are studied in secure communication.Firstly, the realization of chaotic secure communication based on the method of interval synchronization-recalling memory is provided, and the signal can be recovered wholly and exactly. Secondly, the scheme of hyperchaotic secure communication is studied based on state observation. The method enhances the security and is prone to realize in fact with broad applicability. Thirdly, spatiotemporal chaotic sequences are achieved using the two-way coupled map lattice system. And then the improved spatiotemporal chaotic sequences are successfully applied in encrypt method of digital image.