The Research Of Nonlinear Hyperchaos System Synchronization

As a special form of the nonlinear dynamic system, hyperchaotic system provides a strong basis for explaining the phenomenon of nature since it was found. And it has been gradually in transition from theoretical research to practical engineering. It has the widespread application in a secret signal communication, neural network and image processing related field due to its complex dynamic properties such as extreme sensitivity to initial value and the movement of the randomness in the characteristics. However, multidimensional hyperchaotic Qi system has 2 or more is Lyapunov index compared with ordinary chaos system, which makes its trajectory of the multiple direction of separation state phases orbit, and it has more complex dynamic characteristics. Currently for the synchronization of chaotic motion control has made a lot of research results, but the synchronization of hyperchaos system control theory has not formed system. It has a wider range of its potential application value and need to be further in-depth study.This paper is based on the four dimensional autonomous hyperchaotic Qi system and hyperchaotic Liu system as the research object, analysis the nonlinear dynamic characteristics through the theory and equilibrium points stability. And get attractor three-dimensional figure and two-dimensional phase diagram through the numerical calculation.Based on state observer synchronization method and feedback synchronization method,according to the theory of lyapunov stability theorem and synchronization, we design a suitable controller to achieve the same structure of generalized projective synchronization and the anti-synchronization with the same structure for two hyperchaos system respectively.Besides, Feedback synchronization method is used to realize two hyperchaos system under different initial conditions of different structure of synchronization and we obtained by theoretical calculation and numerical simulation respectively corresponding synchronous curve and error curve,and it proves that these two kinds of synchronization methods are effective and feasible. We also compared the two methods of chaotic synchronization, To the same system, the speed of realizing synchronization by using feedback the method is faster than the observer method.On the basis of circuit principle, We designed the four-dimensional hyperchaos Liu system simulated circuit which consists of multiplier, reverse phase summation, inverting circuit and integral circuit. We validate the correctness of circuit design through circuit simulation results by experiment and numerical simulation results are the same.