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In this paper, we show that the dynamics of a wide variety of nonlinearsystems such as engineering, physical, chemical, biological, and ecologicalsystems, can be simulated or modeled by the dynamics of memristor circuits. Ithas the advantage that we can apply nonlinear circuit theory to analyze thedynamics of memristor circuits. Applying an external source to these memristorcircuits, they exhibit complex behavior, such as chaos and non-periodicoscillation. If the memristor circuits have an integral invariant, they canexhibit quasi-periodic or non-periodic behavior by the sinusoidal forcing.Their behavior greatly depends on the initial conditions, the parameters, andthe maximum step size of the numerical integration. Furthermore, an overflow islikely to occur due to the numerical instability in long-time simulations. Inorder to generate a non-periodic oscillation, we have to choose the initialconditions, the parameters, and the maximum step size, carefully. We also showthat we can reconstruct chaotic attractors by using the terminal voltage andcurrent of the memristor. Furthermore, in many memristor circuits, the activememristor switches between passive and active modes of operation, depending onits terminal voltage. We can measure its complexity order by defining thebinary coding for the operation modes. By using this coding, we show that inthe forced memristor Toda lattice equations, the memristor's operation modesexhibit the higher complexity. Furthermore, in the memristor Chua circuit, thememristor has the special operation modes.

Memristor Circuits for Simulating Nonlinear Dynamics and Their Periodic Forcing