Abstract
Due to the introduction of memristors, the memristor-based nonlinear oscillator circuits readily present the state initial-dependent multistability (or extreme multistability), i.e., coexisting multiple attractors (or coexisting infinitely many attractors). The dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science. Based on these considerations, this paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage-current domain and expounds the multistability control strategy. Then, this paper introduces the accurate flux-charge constitutive relation of memristors. Afterwards, the dimensionality reduction modeling method of the memristive circuits, i.e., the incremental flux-charge analysis method, is emphatically introduced, whose core idea is to implement the explicit expressions of the initial conditions in the flux-charge model and to discuss the feasibility and effectiveness of the multistability reconstitution of the memristive circuits using their flux-charge models. Furthermore, the incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux-charge analysis method. The theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor-coupled system as an example.
Highlights
Due to the introduction of memristors, the memristor-based nonlinear oscillator circuits readily present the state initial-dependent multistability, i.e., coexisting multiple attractors. e dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science
This paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage-current domain and expounds the multistability control strategy. en, this paper introduces the accurate flux-charge constitutive relation of memristors
The incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux-charge analysis method. e theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor-coupled system as an example
Summary
E ideal memristor-based nonlinear circuit or system usually has infinitely many equilibria, and their positions and stabilities are related to the internal state initials of memristors, which indicates the extreme multistability of the memristive circuit or system. Bao et al [88] proposed an ideal flux-controlled memristor-based Chua’s circuit with line equilibrium set and revealed the state initial-dependent extreme multistability phenomenon of the memristive circuit. By introducing an ideal flux-controlled memristor into a threedimensional hypogenertic jerk system, the paper [96] constructed a memristive system with four line equilibria sets, which could produce the extreme multistability phenomenon dependent on the state initial of the memristor and other state initials. By introducing a microperturbation into the memristive circuit, a memristive circuit with no equilibrium was constructed, which could produce the phenomenon of hidden extreme multistability [131]
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