In the last two years, the discrete memristor has been proposed, and it is in the early stages of research. Now, it is particularly important to use various simulation softwares to expand the applications of the discrete memristor model. Based on the difference operator, in this paper, a discrete memristor model with quadratic nonlinearity is constructed. The addition, subtraction, multiplication and division of the discrete memristor mathematical model are clarified, and the charge
qis obtained by combining the discrete-time summation module, thereby realizing the Simulink simulation of the discrete memristor. The simulation results show that the designed memristor meets the three fingerprints of memristor, indicating that the designed discrete memristor belongs to generalized memristor.
Using memristors to construct chaotic systems is one of the current research hotspots, but most of the literature is about the introduction of continuous memristors into continuous chaotic systems. In this paper, the obtained discrete memristor is introduced into a three-dimensional chaotic map which is mentioned in a Sprott’s book titled as
Chaos and Time-Series Analysis, and a new four-dimensional memristor chaotic map is designed. Meanwhile, the Simulink model of the chaotic map is established. It is found that attractors with different sizes and shapes can be observed by changing the parameters in the Simulink model, indicating that the changes of system parameters and memristor parameters can change the dynamic behavior of the system. The analyses of equilibria and equilibrium stability show that the four-dimensional chaotic map has infinite equilibrium points. The Lyapunov exponent spectra and bifurcation diagrams of the circuit imply that the map can transform between weak chaotic state, chaotic state, and hyperchaotic state. Meanwhile, the multistability and coexisting attractors are analyzed under different initial conditions. Moreover, by comparing the results of measuring the complexity, it is found that the chaotic map with discrete memristor has richer dynamical behaviors and higher complexity than the original map.
From the perspective of system modeling, in this paper the discrete memristor modeling and discrete memristor map designing are discussed based on the Matlab/Simulink. It further verifies the realizability and lays a foundation for the future applications of discrete memristor.
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