Research On Synchronization Control Of Delayed Chaotic Systems

Three-dimensional chaotic system can only produce one positive Lyapunov exponent. Though it’s structure is simple, it has the disadvantage of degraded secrecy performance. In this paper, we will study a new class of time delay system. Since its solution is illustrated in infinite-dimensional spaces, if the structural dimension are invariable, the dynamic behavior of the new system, compared with the original system, will become more complicated. Therefore, the this new system will promote the confidentiality during the secure communication on the basis of relatively simple system structure, which promises it broad prospects in the filed of security secrecy. The thesis makes time-delayed chaotic system the object of the research, studying this topic from the aspects of its structures, synchronization, and the application in secure communication. The main works and innovative points of this paper are as follows:(1)Construction of New time-delayed systems and the judgement of chaotic characteristics.There are mainly three methods to build the time-delayed system. First, introduce time-delayed control term to the original chaotic system. Second, add time delay linear perturbation terms to the original chaotic systems. Third, adjust the non-delayed term to a delayed one. By constructing three new class of time-delayed systems respectively according to the three methods above, we can tell intuitively whether this new system is chaotic or not at present through its two-dimensional and three-dimensional phase diagrams, power spectrum, time histories and the sensitivity to the initial value figures.And then, this paper analyses the stability of system equilibrium and the dynamic system properties, proving that the system is in a state of chaos in the angle of quantification.(2)Self-time-delayed synchronization of the new time-delayed chaotic systemAccording to the theory of Lyapunov functionals, we can building a suitable controller to realize the self-delayed synchronization of chaotic systems. Since the designed controller has already been proved in theory through the Lyapunov-krasovskii functional, by using the Matlab software,we’ve got the numerical simulation results which proves the feasibility of the algorithm.(3)Synchronization of time-delayed chaotic systems with different dimension and different structureTaking the three-dimensional time-delayed chaotic synchronization as the basis of the research, by using the theory of different-structure systems synchronization, Rossler hyperchaotic system, as the response system, takes new time-delayed chaotic system as the drive system to make synchronization of the two different dimension and different structure systems come true through the design of the synchronization controller. Through the Matlab software, the numerical simulation results demonstrate the feasibility of the algorithm.(4)Exponential synchronization and applications in secure communications of time-delayed chaotic systemsThe sufficient condition of the controller, derived from the related theories of the Lyapunov stability theory and linear matrix inequalities, has posed a design plan of the related controller to discuss the exponential synchronization of new time-delayed chaotic system. Through the theoretical analysis of the main chaotic secure communication technologies,we’ve designed the response of secure communication scheme on the basis of chaotic masking technology, the numerical simulation verified the effectiveness of this scheme.