| The memristive chaotic system is a typical nonlinear system, which has extremely complex dynamic behavior due to the unique physical phenomena such as the sensitive to initial conditions and system parameters, transient chaos, multi-hidden attractor coexistence and state transition, and can provide an updated effective path for the chaotic confidential communications and practical engineering applications. The research content of this dissertation has certain innovation and practicality, and the main results are as follows:(1) A four-dimensional memristive chaotic system is proposed, and its application in image encryption is realized.An improved three-dimensional chaotic system is proposed, and a new hyperbolic memristor model is designed. The new hyperbolic magnetic controlled memristor model is introduced into the three-dimensional chaotic system, and the four-dimensional memristive chaotic circuit with the memristor is deduced. The phase trajectory, bifurcation and Lyapunov exponent spectrum of the new system are drawn and the chaotic evolution of the system with different parameters is analyzed. Further, the hardware experiment circuit board is constructed, and the experimental results are in agreement with the simulation.Finally, the chaotic sequence of the new system is used to encrypt the image, and the encryption histogram, adjacent pixel correlation, anti-attack capability and key sensitivity are analyzed. The results show that the memristive chaotic system has good effect on image encryption.(2) A chaotic oscillation circuit with two hyperbolic memristors is designed, and its multi-stable coexistence motions are also developed.Combined with the classic Chua’s circuit, the chaotic oscillation circuit with two hyperbolic memristors is designed. The operating state of the system with the various parameters and the initial state of the memristor is studied. It is proved that the proposed dual memristor system not only depends on the change of circuit parameters, but also depends on the initial conditions of the system. In addition, the new system also has more hidden attractant coexistence motions including different structural chaotic and periodic motions, up to 12 kinds of motions can be achieved. Furthermore, based on the amplitude amplification method, a new method of effective multi-steady-state search is given, which shows a high consistency between the search result and the numerical simulation.(3) The projective synchronization and complete sunchronization between dual-memristor chaotic systems with the same structure and different initial conditions are realized.According to the stability theory of Lyapunov, a linear feedback controller is designed,and the linear synchronization between the dual-memristor chaotic systems of the same structure is realized. The control scheme is simple, effective and easy to implement, and the driving response fitting curve shows a good linear characteristic of the system.Furthermore, an active synchronization controller for two dual-memristor chaotic systems with different initial values is designed, and the error stability analysis of dual-memristor chaotic systems is carried out. The results show that the designed active synchronization control method can achieve the generalized projection synchronization of the memristive chaotic system with different initial conditions. |
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