Abstract
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.
Highlights
Initial condition-dependent extreme multistability, first encountered in several coupled nonlinear dynamical systems [1,2,3], is a coexisting phenomenon of infinitely many attractors for a given set of system parameters
This paper investigates extreme multistability and its controllability for an ideal voltage-controlled memristor emulator-based canonical Chua’s circuit
Due to the existence of infinitely many equilibrium points, for example, line equilibrium point or plane equilibrium point, this special dynamical phenomenon of extreme multistability is naturally exhibited in a class of ideal flux/voltage-controlled memristor-based chaotic circuits/systems [4,5,6,7,8,9], thereby leading to the emergence of infinitely many disconnected attractors
Summary
Initial condition-dependent extreme multistability, first encountered in several coupled nonlinear dynamical systems [1,2,3], is a coexisting phenomenon of infinitely many attractors for a given set of system parameters. To direct the nonlinear dynamical circuit or system to a desired oscillating mode, an effective control approach should be proposed [12] To this end, this paper takes an ideal voltage-controlled memristor emulator-based canonical Chua’s circuit as an example; a controllable strategy for extreme multistability is achieved through converting the initial condition-dependent dynamics in the voltage-current domain into the system parameter-associated dynamics in the flux-charge domain [29, 30]. With the accurate constitutive relation, an incremental flux-charge model for the memristor-based canonical Chua’s circuit is constructed, upon which all the initial conditions in the voltage-current model can be explicitly formulated by the system parameters in the flux-charge model and the multiple stable states can be controlled by changing the initial condition-related system parameters.
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