Control And Synchronization Of Low-mode Couette-Taylor Flow System

Chaos is one of the key problems in the field of nonlinear dynamics.Since the synchronization of chaos has great potential and development prospects in the engineering field,the research of chaotic systems has become the core of scholars at home and abroad.Chaotic synchronization is to make two chaotic systems vibrate in a synchronization manner.Generally,the dynamic behavior of two chaotic systems is the same when the initial conditions are close,and the second system is driven by the first system(drive-response method).The synchronization of chaotic systems has important application prospects in many systems such as chemistry,biology,geography,Couette-Taylor flow,especially in secure communication.Based on years of research by previous researchers,this paper mainly studies the synchronization of Couette-Taylor flow system:(1)The basic dynamic characteristics of Couette-Taylor flow system are studied and the whole process of system chaos is simulated numerically.The universal characteristics of system's chaotic behavior are revealed by using phase diagram,Lyapunov exponent spectrum,bifurcation diagram,Poincare section and power spectrum.Based on the Lyapunov stability theory,by designing an adaptive controller,the adaptive synchronization of Couette-Taylor flow system with uncertain parameters,time-delay and fractional-order synchronization of system are realized.Finally,the correctness and superiority of the proposed method are verified by MATLAB software simulation.(2)A new four-mode hyperchaotic Couette-Taylor flow system is proposed,and the phase diagram projection of new system is obtained by numerical simulation.Globally exponentially attractive set and positive invariant set of the system are discussed.The adaptive control for synchronization of the hyperchaotic Couette-Taylor flow system with uncertain parameters and time-delay via a single variable is achieved.Finally,the numerical simulation is carried out by using MATLAB software,and the simulation results strictly verify the authenticity of the proposed method.(3)The problem of synchronization for a class of chaotic systems with uncertain parameters and external disturbances is studied by using the method of order expansion.Based on the active control method and the Lyapunov stability theorem,a controller is designed to realize the synchronization of chaotic systems with different orders.The method has been applied to solve the synchronization problem of unified hyperchaotic system and Couette-Taylor three modes system.Numerical simulations show the effectiveness of the method.