Chaotic Modelling Based On Memristor

Memristor (Memory resistor), which is proposed by professor L. O. Chua (American Scientist of Chinese) originally in1971and found by R. Stanley Williams of HP lab in2008, is the fourth fundamental circuit element. This milestone discovery had published in Nature in the same year.Memristor is a circuit element controlled by charge and flux. It has potential applications in computer memory and artificial neural network because of its nano-scale and memory properties. Memristor also possesses complex dynamics which make memristor-based circuit generate special dynamical behaviors such as chaos. Chaos is a complicated dynamical phenomenon with some specific characteristics includes sensitive to the initial conditions and system parameters, orbits confined in the finite region of phase space etc. Generally, chaos is accompanied with bifurcation and fractals, these interesting dynamical phenomena are wildly used in Mechatronics, Ecology, Aeronautics and Economics.Therefore, according to the memristor’s properties and chaotic modeling approach, this thesis studies memristor-based non-linear circuit and system models, and investigates their chaotic features. The main contents of the thesis are demonstrated as following:1. Study chaotic model of time-delay memristive circuitDesign a new type of time-delay memristive circuit based on circuit theory. Study memristive circuit’s time-delay effect by analyzing mathematic model and equilibrium points, computing phase map, calculating Lyapunov exponents and spectrum, simulating bifurcation behaviors.2. Study a memristor’s analog-circuitDevise an analog-circuit on the basis of memristor’s features to simulate memristor’s dynamical behavior. Design a chaotic circuit based on this analog-circuit to verify its non-linear characteristics. The computer numerically simulation results valid that the analog-circuit emulates memristor effectively and efficiently.3. Study the united model of chaotic circuit and systemPropose a new united model of chaotic circuit and system based on classic chaotic circuit and system. Bridge the gap between chaotic systems and chaotic circuits. Meanwhile, use the united model to predict and deduce new chaotic systems. The numerically emulation results valid their chaotic features and verify the united model’s effectiveness.