Chua Corsage Memristor: Phase Portraits, Basin of Attraction, and Coexisting Pinched Hysteresis Loops

Abstract

The Chua Corsage Memristor is the simplest example of a passive but locally active memristor endowed with two asymptotically stable equilibrium points [Formula: see text] and [Formula: see text] when powered by an E-volt battery, where [Formula: see text]. The basin of attraction is defined by [Formula: see text], [Formula: see text] for [Formula: see text], and [Formula: see text], [Formula: see text] for [Formula: see text]. By adding an inductor of appropriate value [Formula: see text] in series with the battery, the resulting circuit undergoes a supercritical Hopf bifurcation and becomes an oscillator for [Formula: see text]. Applying a sinusoidal voltage source [Formula: see text] across the Chua corsage memristor, one finds two distinct coexisting stable periodic responses, depicted by their associated pinched hysteresis loops, of the same frequency [Formula: see text] whose basin of attraction is defined by [Formula: see text], and [Formula: see text], respectively, where [Formula: see text] depends on both amplitude A and frequency f. An in-depth and comprehensive analysis of the above global nonlinear phenomena is presented using tools from nonlinear circuit theory, such as Chua’s dynamic route method, and from nonlinear dynamics, such as phase portrait analysis and bifurcation theory.

Nonlinear Dynamics, Switching Kinetics and Physical Realization of the Family of Chua Corsage Memristors

“…It is considered as one of the most promising element in emerging memory sector [4][5][6] and neural applications [7,8], due to its propitious attributes under DC or AC excitation and miniature nanoscale physical dimension along with synapse alike operation. Recently, numerous research activities are ongoing on binary and multistate phenomena in generic and extended memristors [9][10][11][12][13][14][15][16] which could lead to another stage of technical innovation 2 of 19 in the memristor area. Nonlinear dynamics theory, and circuit and system theoretic concepts can be devoted to explaining the principle of the multistate memristors [9].…”

“…The DC V-I curves of CCMs have an explicit analytical equation with its parametric representation that rarely happens. In addition, each member of CCM family exhibits a negative slope region on its DC V-I curve which give rise to complexity by exploiting local activity; and complex phenomenon and information processing might emerge over the parameter ranges of CCMs either operating on or near the neighborhood of its edge of chaos domain [12][13][14][15][16].…”

“…The locally active CCM family exhibit asymptotical stability via the supercritical Hopf bifurcation [13][14][15][16]. The state altering of CCMs follows the nonlinear dynamic route of a chosen initial state x n (0) and repeats until the state reaches in a particularly stable state which is termed as an "attractor".…”

“…The state altering of CCMs follows the nonlinear dynamic route of a chosen initial state x n (0) and repeats until the state reaches in a particularly stable state which is termed as an "attractor". The state space of CCMs contain various attractors, and each attractor has its own basin of attraction [13][14][15][16]. The equilibrium state of these type of memristors moves by the amount of time integral of applied inputs or noises that are applied at a stable equilibrium state.…”

“…The equilibrium state of these type of memristors moves by the amount of time integral of applied inputs or noises that are applied at a stable equilibrium state. However, the state of CCMs returns back to its original equilibrium state (attractor), unless the state moves beyond the boundary of the current basin of attraction [13][14][15][16]. Therefore, it can be utilized as a robust bistable or multistate memory device.…”