Research On Some Autonomous Chaotic System's Synchronous Method

Nowadays, chaos has been intensively studied within physics, mathematics and so on. It has been realized that chaos research has great potential in many technological disciplines. The synchronous method of chaotic system is studied in this thesis using the methods of theoretical derivation and numerical simulation. The main achievements contained in the research are as follows:(1) For parts of chaotic systems can't achieve synchronization by P-C method, the author proposed a solution, namely rotational coordinate transformation method. For rotational coordinate transformation is a linear transformation, it not only can't change the properties of the chaotic system, but also can let the chaotic system achieve synchronization by P-C method after rotational coordinate transformation, such method increase the applicability of P-C synchronization. The transformed chaotic system may be complex in structure. However, in practical chaotic secure communication, the transformed drive-response systems can be constructed at the sender and receiver respectively, which can be synchronized by the sender sending a single signal. This is meaningful to chaotic secure communication.(2) The article analyses some new high-dimensional chaotic system. The article first researches the adaptive synchronization and parameters identification of a new four-dimensional chaotic system which proposed by Qi. The author designes an adaptive controller and the update rule of the parameters. It is proved theoretically that the controller can make the states of the drive system and the response system with unknown system parameters asymptotically synchronized, and identify the response system's unknown parameters. Then the author designs a nonlinear active controller aiming at hyperchaotic Lorenz system. The controller can effectively implement the chaotic tracking of hyperchaotic Lorenz system to arbitrary referrence signals the method can be applied to other chaotic systems. Furthermore it can be extended to track more variables.(3) Aims at the complication of constructing response system, according to the principium of projective synchronization, the author deduce the response system's general formula and realizes the projective synchronization of some chaotic systems. It simplified the process of projective system. The author chooses three representative systems to make simulate experiment. The result shows us: all systems achieve projective synchronization in a short time. The result of the simulation also proves the correctness of the method.