Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

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.

An efficient image encryption algorithm using a discrete memory-based logistic map with deep neural network

“…A memristor is a fundamental circuit unit with memory that illustrates the connection between charge and magnetic flux. Furthermore, memristors have numerous applications, including neural networks [12], electrical engineering [13][14][15], secure communication [16], and so on. Classic chaotic maps, such as the logistic and henon maps, frequently suffer from a narrow parameter range and low complexity.…”

Initial-condition effects on ReLU-type hyper-jerk system and its application in image encryption

“…Memductance functions can often be split into two categories: smooth functions and non-smooth functions. Many memristor-based circuits and systems are explored using some conventional smooth functions, such as the hyperbolic tangent (Tanh) memductance function [12,19], quadric memductance function [20], sine memductance function [21], and others [22]. Absolute value memductance function is a common non-smooth function, and is often used to construct novel memristive system [23].…”

“…Since the innate memory characteristic of the memristor [11], the memristive nonlinear circuits and systems effortlessly display state initial-dependent multistability [27] or extreme multistability [28][29][30]. In actuality, extreme multistability mainly follows an unabridged smooth bifurcation route in regard to the initial conditions intuitively, and the bifurcation trajectories progressively changed [22]. The majority of recently published work, however, only concentrates on the extreme multistability connected to the memristor initial conditions (MIC) [22,31,32], and scarcely touches on the nonmemristor initial conditions (NMIC) [12].…”

“…In actuality, extreme multistability mainly follows an unabridged smooth bifurcation route in regard to the initial conditions intuitively, and the bifurcation trajectories progressively changed [22]. The majority of recently published work, however, only concentrates on the extreme multistability connected to the memristor initial conditions (MIC) [22,31,32], and scarcely touches on the nonmemristor initial conditions (NMIC) [12]. To explore the intricate dynamics brought on by the memristors and non-memristors initial conditions, we present a novel memristive hyper-jerk system with a non-smooth ReLU memductance function in this article.…”

Two Modified Chaotic Maps Based on Discrete Memristor Model

“…In hardware implementation of memristors, remarkable work has been carried out [4][5][6][7][8][9]. Moreover, the memristor is applied in many fields such as neural networks [10][11][12], electrical engineering [13][14][15], secure communications [16], etc.…”