Mapping equivalent approach to analysis and realization of memristor-based dynamical circuit

Abstract

A novel mapping equivalent approach is proposed in this paper, which can be used for analyzing and realizing a memristor-based dynamical circuit equivalently by a nonlinear dynamical circuit with the same topologies and circuit parameters. A memristor-based chaotic circuit and the corresponding Chua's chaotic circuit with two output differentiators are taken as examples to illustrate this approach. Equivalent dynamical analysis and realization of the memristor-based chaotic circuit are performed by using Chua's chaotic circuit. The results indicate that the outputs of memristor-based chaotic circuit and the corresponding outputs of Chua's chaotic circuit have identical dynamics. The proposed approach verified by numerical simulations and experimental observations is useful in designing and analyzing memristor-based dynamical circuits.

An Improved Memristive Diode Bridge‐Based Band Pass Filter Chaotic Circuit

“…Numerous memristive dynamical circuits have been reported by introducing memristor into classical linear or nonlinear dynamical circuits [4,5,9,13,14,16,[20][21][22][23], from which complex dynamical behaviors, such as chaotic behaviors [4,5,20,21], coexisting multiple attractors [9,13], selfexcited and hidden attractors [14,22,23], and chaotic and periodic bursting [16], have been revealed and analyzed by theoretical analyses, numerical simulations, and experimental measurements. It is worth noting that the stability depends on the memristor initial condition in a memristive dynamical circuit, leading to the occurrence of coexisting multiple attractors [9,13].…”

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

“…The ideal voltage-controlled memristor emulator is equivalently implemented with an electronic circuit via op-amp integrators and analog multipliers [5,6,34], as shown in Figure 1(b). In our next work, the considered circuit parameters remained unchanged and are listed in Table 1, where is the total gain of two multipliers and .…”

“…Flux-charge analysis method was first postulated as a tool of dimensionality reduction [31][32][33][34][35][36], in which the initial conditions of the memristor-based circuit or system are not precisely formulated, thereby leading to the absence of the initial condition-dependent dynamical behaviors [34][35][36]. In the last two years, a new flux-charge analysis method is reported in [29,30], which judiciously utilizes the incremental flux and charge to substitute the conventional flux and charge and efficaciously solves the issue of the original fluxcharge analysis method.…”

Coexisting attractors in a memcapacitor-based chaotic oscillator

“…However, the interest in memristive systems has not grown rapidly until a solidstate memristor was developed by Hewlett-Packard in 2008 [2]. Because of particular nonlinear characteristics of a memristor, it is widely employed to generate chaos by replacing nonlinear resistance elements in classic chaotic circuits, and some novel dynamic behaviors could be observed [3][4][5][6]. Recently, memristors are also used to compose and improve neural networks.…”