Chua Corsage Memristor Oscillator via Hopf Bifurcation

Abstract

This paper demonstrates that the Chua Corsage Memristor, when connected in series with an inductor and a battery, oscillates about a locally-active operating point located on the memristor’s DC [Formula: see text]–[Formula: see text] curve. On the operating point, a small-signal equivalent circuit is derived via a Taylor series expansion. The small-signal admittance [Formula: see text] is derived from the small-signal equivalent circuit and the value of inductance is determined at a frequency where the real part of the admittance [Formula: see text] of the small-signal equivalent circuit of Chua Corsage Memristor is zero. Oscillation of the circuit is analyzed via an in-depth application of the theory of Local Activity, Edge of Chaos and the Hopf-bifurcation.

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.…”