Flux–Charge Analysis of Two-Memristor-Based Chua's Circuit: Dimensionality Decreasing Model for Detecting Extreme Multistability

Abstract

In this paper, from a new perspective of flux and charge, we present in-depth analyses of two ideal memristor emulators and the fifth-order memristive Chua's circuit constructed based on them. The constitutive flux–charge relations of the two adopted memristor emulators are first formulated, and their initial-dependent characteristics are numerically revealed and experimentally verified. Thereafter, with these two constitutive relations, a third-order dimensionality decreasing flux–charge model for the fifth-order memristive Chua's circuit is constructed, in which five extra constant system parameters are introduced to indicate the initial states of the five dynamic elements. Numerical simulations confirm that this newly constructed model possesses several determined equilibria and maintains the initial-dependent dynamics of the original voltage–current model. Thus, the complex and sensitive initial state-related extreme multistability phenomenon can be deeply explored through theoretical analyses and hardware measurements. It is demonstrated that the sensitive extreme multistability phenomenon becomes detectable in the flux–charge domain, which is efficient for exploring the inner mechanisms and further seeking possible applications of this special phenomenon.