| Chaos is a kind of special and complex behavior embodied in motion of nonlinear systems.The theory of studying the law of chaotic motion is one of the most important theoretical achievements of the last century.As the key technology of applying chaos theory,chaos synchronization has attracted much attention for more than 30 years since it was discovered,especially in the fields of image,audio encryption,and confidential transmission of signals.As a new nonlinear element with memory function,memristor can make the circuit show complex chaotic characteristics.Combined with fractional calculus theory with wide application value,the research on the synchronization of fractional memristor chaotic system is undoubtedly a direction with important research value and application prospect.This paper studies the dynamic characteristics of a class of fractional memristor chaotic systems,and realizes several synchronization schemes combined with numerical simulation and circuit simulation.The concrete contents of the research are detailed as follows:Firstly,a memristor chaotic oscillators with rich chaotic characteristics is extended to fractional order to obtain fractional-order memristor chaotic systems.Taking the obtained fractional-order memristor chaotic system as topic,and the study of dynamic characteristics from the aspects of equilibrium and stability,bifurcation diagram,Poincare map and Lyapunov exponent spectrum is conducted.Then,based on the combination of theoretical analysis and numerical simulation,a nonlinear feedback controller with adjustable parameters is designed.Different types of synchronization,including complete synchronization,anti-synchronization and projective synchronization,can be achieved by adjusting a single control parameter.Secondly,a novel fractional integral sliding-mode surface with short convergence time is designed,which can make the synchronization error system reach the origin of state space in a finite time.Then,when the response system parameters have complete uncertainty,finite-time unknown parameter adaptive law and the sliding-mode-based adaptive finite-time synchronization controller are designed,and the sufficient condition for the synchronization error system to reach the sliding mode surface and the identification of unknown parameters can be realized in limited time are obtained.The simulation results of four-dimension system movement trajectories,error curves and parameter identification curves show that the designed synchronization strategy can realize the adaptive finite-time sliding-mode generalized projective synchronization and the identification of unknown parameters of fractional memristor chaotic system in limited time.Finally,based on fractional hybrid circuit unit,the circuit design and Simulation of fractional memristor chaotic system are carried out.The rich chaotic characteristics of the system can be observed through oscilloscope,which verifies the physical realizability of fractional memristor chaotic circuit.Then,with fractional memristor chaotic system and fractional Liu system as driving systems respectively,the controller based on active control principle is designed for realizing the synchronization of the two systems with different dimensions and different structures.The circuits for the two systems with different structures realizing synchronization by the methods of dimension reduction and dimension increase respectively are designed for simulation experiments,and the effectiveness of the designed controller is verified by observing the waveforms of the error system with a four-channel filter. |
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