The Study Of Fractional Order Generalized Augmented Lü (Hyper)Chaotic System And Its Application In Secure Communication

Due to its complex characteristics, such as extremely sensitive to initial conditions, inherent randomness, ergodicity, continuous broadband spectrum and so forth, chaotic system has great development prospect in secure communication and other fields. Compared with the integer order chaotic system, the fractional order chaotic system has more complex dynamics characteristics and larger key space, which is safer and more reliable when it is applied in the communication encryption. Therefore, the study of fractional chaotic system and its application in secure communication is of great importance both in theory and in practice.Based on the integer order generalized augmented Lu system, the fractional order generalized augmented Lu system(hyperchaotic generalized augmented Lu system) and its synchronization,circuit design and implementation and the application in the secure communication are investigated in this paper.1.With the predictor-corrector method and the frequency domain approximation method, we investigate the dynamics characteristics of a fractional order generalized augmented Lu system and a fractional order hyperchaotic generalized augmented Lu system by analyzing their phase portraits, Poincare sections, bifurcation diagrams, Lyapunov exponent spectra and power spectra, and we find chaos phenomena occur in the fractional order generalized augmented Lu system when fractional order q>0.871 and the system present chaos in a large range of system parameters. Moreover, the system will present four-wing fan shaped chaotic attractors, periodic attractors and quasi-periodic attractors which indicates that there are abundant dynamics behaviors in the chaotic system. we find that the fractional order hyperchaotic generalized augmented Lu system will present chaos when fractional order q>0.805. By drawing its Lyapunov exponent spectra, we can see that the system has two positive Lyapunov exponents in a large range of parameters, which indicate the system presents hyperchaos and its hyperchaotic attractor is four-wing fan shaped when system parameters change in a certain range.2.Research on the synchronization of the fractional order system mentioned above. On the basis of the stability theory of the fractional order linear system, a nonlinear feedback synchronization method is adopted to design the controller to synchronize the fractional order generalized augmented Lu system and it is proved effective through the numerical simulation;while we utilize the one way coupling method to investigate the synchronization of the fractional order hyperchaotic generalized augmented Lu system, the theoretical analysis and the process of derivation are provide to illustrate the feasibility of the synchronization method, and numerical simulation is conducted to verified that feasibility. Furthermore, and the critical value of the coupling coefficient k is obtained in numerical simulation.3.The improved chaotic circuit modular design method is adopted to design and implement the two fractional order system and their synchronization circuit.Through circuit simulation and circuit experiment, we find that the circuit simulation result, circuit experiment result are in accordance with the numerical simulation result, demonstrating that the adopted synchronization methods are effective and feasible.4.Study on the application of the synchronization of fractional order (hyper)chaotic system in secure communication. A secure communication scheme of chaotic masking based on the one-way coupling synchronization of the fractional order hyperchaotic generalized augmented Lii system is designed. The numerical simulation result, the circuit simulation result and the analog circuit experiment result show that the proposed scheme has good secrecy and feasibility.