| Memristor is a kind of nonlinear resistor with memory, it is considered to be the fourth fundamental circuit element besides resistor,inductance and capacitor,it also opens up huge possibilities in the field of information technology,such as artificial intelligence, neural network, new memory, and memristive chaotic circuits. Specially,the generalized memristor is a nonlinear circuit by using common components, which is able to implement fingerprints of memristor equivalently, and it has a simple circuit structure with stable characteristics, consequently its physical implementation is easy,in addition, it shows practical value in monolithic integration. In particular,generalized memristor provides important information for modeling and experiment analysis of the real memristor. Compared with common chaotic circuits, the memristive chaotic circuits built by replacing the Chua's diode in Chua's circuit with memristor show more complex nonlinear behavior and have more value, therefore,it's meaningful to research the dynamical characteristics and synchronization of them.A new 4D memristive circuit is presented in this thesis,and its dynamical characteristics and synchronization are researched through numerical simulations and hardware experiments. Furthermore, a memristive chaotic system without equilibrium is proposed to make comparison analysis. The main content is depicted as follows:(1) The origin,development, definition and basic characteristics of chaos are proposed. Analysis methods to memristive chaotic circuits,and basic information of synchronization are also recommend.(2) A new 4D memristive circuit is formulated, and it shows different motions by changing corresponding negative resistance. Especially, it presents very rich dynamical characteristics as well as easy observation, and its parameters can also be easily adjusted.(3) Based on optimal control, the synchronization of the new 4-dimension memristive circuit is studied, and a general optimal synchronization controller is proposed as well. The sufficient conditions for the synchronization of drive system and response system is proved by Lyapunov stability theorem. With this method,the optimization on both energy consumption and synchronization error could be realized synthetically. The reliability of the proposed method is proved by all simulation results.(4) A new memristive system without equilibrium is presented at last, and its behavior is analyzed through Lyapunov exponents, bifurcation diagram, and phase portraits. The circuital implementation confirmed the chaos dynamical. Especially the system shows different dynamical behavior compared with the above-mentioned new 4-dimension memristive circuit. |
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