Memristor-Based Canonical Chua’s Circuit: Extreme Multistability in Voltage-Current Domain and Its Controllability in Flux-Charge Domain

This paper investigates extreme multistability and its controllability for an ideal voltage-controlled memristor emulator-based canonical Chua’s circuit. With the voltage-current model, the initial condition-dependent extreme multistability is explored through analyzing the stability distribution of line equilibrium point and then the coexisting infinitely many attractors are numerically uncovered in such a memristive circuit by the attraction basin and phase portraits. Furthermore, based on the accurate constitutive relation of the memristor emulator, a set of incremental flux-charge describing equations for the memristor-based canonical Chua’s circuit are formulated and a dimensionality reduction model is thus established. As a result, the initial condition-dependent dynamics in the voltage-current domain is converted into the system parameter-associated dynamics in the flux-charge domain, which is confirmed by numerical simulations and circuit simulations. Therefore, a controllable strategy for extreme multistability can be expediently implemented, which is greatly significant for seeking chaos-based engineering applications of multistable memristive circuits.

HYPERCHAOS IN A MEMRISTOR-BASED MODIFIED CANONICAL CHUA'S CIRCUIT

After the successful solid state implementation of the memristor, memristor-based circuits have received a lot of attention. In this paper, a memristor with cubic nonlinear characteristics is employed in the modified canonical Chua's circuit. A systematic study of hyperchaotic behavior in this circuit is performed with the help of nonlinear tools such as Lyapunov exponents, phase portraits and bifurcation diagrams. In particular, an imitative memristor circuit is examined to reveal the construction of hyperchaotic attractors.