PSPICE models of current- and flux-controlled meminductor are described. The models consist of two parts, one of which represents the state-space description of the memory effect of the device, and the other part is an inductor whose inductance depends on the system state. The basic fingerprints of the meminductor, i.e. the flux–current pinched hysteresis loops, the unambiguous constitutive relation between the time integral of flux and electric charge, and identical zero-crossing points of flux and current waveforms are demonstrated on the example of current-controlled meminductor.

In order to avoid non-convergence and other numerical problems associated with the simulation of extremely large memristive networks, suitable models of the individual memristors need to be developed. A circuit containing thousands of memristors for finding the shortest path in a complicated maze is a typical example of a numerically challenging simulation. A benchmark circuit for testing the applications of various complexities is used for the transient analysis. It is shown that various commonly used models, from simple behavioral to Pickett models, require special modifications for minimizing the simulation time and improving the convergence issue.

The paper introduces a set of models of memristive devices for a reliable, accurate and fast analysis of large networks in the SPICE (Simulation Program with Integrated Circuit Emphasis) environment. The modeling starts from the recently introduced TEAM (ThrEshold Adaptive Memristor Model) and VTEAM (Voltage ThrEshold Adaptive Memristor Model). A number of improvements are made towards the stick effect elimination and other numerical refinements to make the analysis of large networks fast and accurate. A set of models are proposed that utilize the synergy of several techniques such as window asymmetrization, integration with saturation, state equation preprocessing, scaling, and smoothing. The performance of models is tested in Cadence PSPICE 17.2 and particularly in HSPICE v2017, the latter on a large-scale CNN (Cellular Nonlinear Network) for detecting edges of binary images. The simulations manifest the usability of developed models for fast and reliable operation in networks containing more than one million nodes.

Two-ports for mutual transformation between flux-controlled memristors and charge-controlled memristors are proposed. Attention is paid to memristors with the region of negative differential memristance in the charge-flux constitutive relation, when such a transformation should be made carefully. Connections between this transformation, duality rules, and Chua’s table of higher-order elements are described. The proposed transforming cells can be made up of commercially available integrated circuits. Their proper operation is demonstrated via simulations and lab experiments with memristive oscillators.