Synchronization Of Fractional-order Chaotic Systems And Its Application In Secure Communication

Chaos has been one of the key research in the field of deterministic nonlinearscience, compared to the signals of integer order chaotic behavior, the fractional-orderchaotic is more complex, which have a great of potential and development prospectsfor applications in secure communications engineering and other fields. Chaotic mas-king techniques required to send a useful signal superimposed on the chaotic signal inthe formation of mixed-signal, with strong security in the transmission process, manyresearchers focus only simple periodic chaotic signal as transmission, less focus onthe complex non-periodic signal with little real practical application.In this paper,some problems about chaotic synchronization and its application insecure communication were studied by numerical simulation based on the calculestheory of fractional order.The main work can be summarized as follows:(1) Base on fractional-order differential operators and the complex domain repres-entation method, this paper studied the fractional-order R ssler chaotic system, thechaotic system is implemented by the dynamic simulation model of this system, andthe parameter and structure of its circuit is designed. It is verified that chaos exists inthe fractional-order R ssler chaotic system is2.7by the model of dynamic simulationand its circuit.(2) Based on fractional-order differential operators and the complex domain repre-sentation method, two ways synchronization of fractional order Chen system is stud-ied about its commensurate and incommensurate forms, and the synchronization withtwo identical commensurate system and two identical incommensurate systems isrealized by designing the suitable active controller, respectively.(3) A new controller design method to synchronize the non-integer-order hyper-chaotic system is proposed, the synchronization between the two identical fractionalorder hyperchaotic Chen systems, which its nonlinear terms are divided into stability-related part and stability-unrelated part, is realized and appplication to securecommunication by designing the suitable controller in stability-related part,havemuch simpler structures than those of existing results in liternature.(4) A new controller design method with the synchronization of the fractional order hyperchaotic system is proposed, the synchronization between two identicalfractional-order Chen hyperchaotic systems is realized by designing only two suitablecontrollers in the response system. Furthermore, this control scheme can be used insecure communication via the technology of chaotic masking using the complexnon-periodic information as trial message, and the useful information can be recove-red at the receiver. Numerical simulations coincide with the theoretical analysisresults demonstrate the effectiveness and feasibility of the proposed method.