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

This article reviews the nonlinear dynamical attributes, switching kinetics, bifurcation analysis, and physical realization of a family of generic memristors, namely, Chua corsage memristors (CCM). CCM family contains three 1-st order generic memristor dubbed as 2-lobe, 4-lobe, and 6-lobe Chua corsage memristors and can be distinguished in accordance with their asymptotic stable states. The 2-lobe CCM has two asymptotically stable equilibrium states and regarded as a binary memory device. In contrast, the versatile 4-lobe CCM and 6-lobe CCM are regarded as a multi-bit-per-cell memory device as they exhibit three and four asymptotic stable states, respectively, on their complex and diversified dynamic routes. Due to the diversified dynamic routes, the CC memristors exhibit a highly nonlinear DC V-I curve. Unlike most published highly-nonlinear DC V-I curves with several disconnected branches, the DC V-I curves of CCMs are contiguous along with a locally active negative slope region. Moreover, the DC V-I curves and parametric representations of the CCMs are explicitly analytical. Switching kinetics of the CCM family can be demonstrated with universal formulas of exponential state trajectories xn(t), time period tfn, and applied minimum pulse amplitude VA and width Δw. These formulas are regarded universal as they can be applied to any piecewise linear dynamic routes for any DC or pulse input and with any number of segments. When local activity, and bifurcation and chaos theorems are employed, CMMs exhibit unique stable limit cycles spawn from a supercritical Hopf bifurcation along with static attractors. In addition, the nonlinear circuit and system theoretic approach is applied to explain the asymptotic stability behavior of CCMs and to design real memristor emulators using off-the-shelf circuit components.