| Chaos motion which is a special movement of the nonlinear dynamic exists in every area of nature. As chaos control has been widely used in biology, fluid mechanic,power system and secure communication, etc. Chaos has attracted many scholars’ attention since it was found. This article studies on three different chaotic systems respectively. The main contributions are as follows.① The article introduces the mathematical model of a class of fractional order chaotic systems with unknown parameters. Then it designs a appropriate controller and adaptive law of the parameters, which make the system can track to any given signal.Finally, the simulation of fractional order Newton-Leipnik system are presented to show the efficiency of the conclusion.②Based on the Lyapunov stability theory, the paper adds an impulse control to the general mathematical model of 3D complex chaotic systems, selects a appropriate controller. The exponential stability or asymptotic stability of the system can be achieved when some specific conditions satisfied. The corollaries of exponential stability and asymptotic stability are obtained after considering three kinds of special cases. Further, the paper uses pulse synchronization to synchronize two definite complex chaotic systems. Finally, numerical simulations with Matlab are presented to show the availability of the method.③By taking fractional order complex-variable system as study object, adding pulse and control, selecting the controller reasonably, the essay studies the self-synchronization and synchronization of fractional order complex-variable system with impulsive adaptive method. |
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