Chaos characteristic analysis of fractional nonlinear systems with synchronous control algorithm research
|School||Central South University|
|Course||Electronic Science and Technology|
|Keywords||Chaos Fractional Calculus Simplify the Lorenz system Dynamics Synchronous control|
The fractional nonlinear chaos characteristics of the system and its application is a hotspot in the field of nonlinear science . In this paper, Fractional simplified Lorenz system as the research object , using theoretical analysis and numerical simulation methods studied Fractional simplify the dynamics of the Lorenz system , synchronous control and its applications , and research results with theoretical significance and application value . Using fractional calculus time domain solver based on Matlab simulation platform , from the evolution of the phase diagram of the system , the bifurcation diagram , the largest Lyapunov exponent of the bifurcation and chaotic dynamical behavior of Fractional simplified Lorenz system analysis and Numerical Study . Simulation results show that the order of the system parameters and Fractional can be used as the bifurcation parameter of the system ; Fractional simplify the Lorenz system has a complex and interesting dynamics when the total order of the system is less than 3 and greater than 3:00 ; For different parameters and order , the system generates a chaotic range of different fractional-order simplified Lorenz system to generate chaos minimum order of 2.66 . Respectively using proportional projective synchronization , and generalized projective synchronization function projective synchronization and modified function projective synchronization control algorithm study two different initial fractional simplify the synchronization of the Lorenz system . Based the Roth the - Hall Horowitz guidelines and Lyapunov stability principle derived two fractional projective synchronization of chaotic systems synchronization theorem , the synchronized projection range of control parameters ; analysis of the control parameters of the synchronization system performance the impact of the law . Projective synchronization control method based on Matlab numerical simulation studies show fractional order chaotic system is effective . Simplify the generalized projection of the Lorenz system based on fractional synchronization and modified function projective synchronization , respectively, designed and implemented chaotic masking secure communication scheme . The numerical simulation and performance analysis shows the validity and correctness of secure communication scheme , laid the foundation for the fractional order chaotic system applied research .