Dissertation > Mathematical sciences and chemical > Physics > Theoretical Physics > Nonlinear physics > Chaos Theory

Chaos characteristic analysis of fractional nonlinear systems with synchronous control algorithm research

Author WangXia
Tutor SunKeHui
School Central South University
Course Electronic Science and Technology
Keywords Chaos Fractional Calculus Simplify the Lorenz system Dynamics Synchronous control
CLC O415.5
Type Master's thesis
Year 2010
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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 .

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