Synchronization Of Fractional Chaotic Systems And Application In Security Communication

Chaotic systems always exist in nonlinear dynamic systems, and have been wellstudied in many fields. It’s especially suitable for information encryption, because ofsome features that chaotic system possesses such as highly sensitivity to initialconditions. Fractional calculus is a generalization of integration and differentiation tononinteger order fundamental operator. Considering the fact that the historicalmemory effect for fractional operator, the dynamical behaviors created by fractionalorder system are more complex than that of traditional integer order chaotic system.It has a great potential application in chaotic secure communication. This paperstudies the fractional system, and makes a consideration on the engineeringapplication such as secure communication.Firstly, this paper proposed two methods separately for the control of twofractional chaotic systems. The first method is for a novel fractional three-dimensional automation chaotic system, which can stabilize the fractional chaoticsystem to limit cycle or the equilibrium point of the system based on the differentvalues of control variable. The second method for fractional chen system is afeedback closed-loop control, and has two control parameters，which are systemorder and the time scale factor. At the same time, the paper analyzed the physicalsignificance and the function of the two parameters.Secondly, the paper proposed two methods for the fractional chaoticsynchronization control, one is based on pinning control, the other based on slidingmode control. The paper proposed the definition and principle of pinning control,and proved the effectiveness of the method through the simulation of a novelfractional chaotic system. The procedure of the scheme based on sliding mode control is studying the principle of sliding controller, designing the sliding modesurface, and simulation at last. At the same time, the paper also analyzed the stabilityof the method.At last, the paper studied the secure communication scheme in fractional chaoticsystem. Two schemes are proposed, separately based on chaotic masking andobserver. The paper proved the effectiveness the scheme based on chaotic maskingthrough sine function, and provided the advantages of the scheme. The scheme basedon observer is based on the principle of chaotic modulation. In order to recoversignal, designing suitable observer is to identify the parameters at exponent speed.The fractional chaotic systems are also applied in many fields.