Recent Advances in Dimensionality Reduction Modeling and Multistability Reconstitution of Memristive Circuit

Due to the introduction of memristors, the memristor-based nonlinear oscillator circuits readily present the state initial-dependent multistability (or extreme multistability), i.e., coexisting multiple attractors (or coexisting infinitely many attractors). The dimensionality reduction modeling for a memristive circuit is carried out to realize accurate prediction, quantitative analysis, and physical control of its multistability, which has become one of the hottest research topics in the field of information science. Based on these considerations, this paper briefly reviews the specific multistability phenomenon generating from the memristive circuit in the voltage-current domain and expounds the multistability control strategy. Then, this paper introduces the accurate flux-charge constitutive relation of memristors. Afterwards, the dimensionality reduction modeling method of the memristive circuits, i.e., the incremental flux-charge analysis method, is emphatically introduced, whose core idea is to implement the explicit expressions of the initial conditions in the flux-charge model and to discuss the feasibility and effectiveness of the multistability reconstitution of the memristive circuits using their flux-charge models. Furthermore, the incremental integral transformation method for modeling of the memristive system is reviewed by following the idea of the incremental flux-charge analysis method. The theory and application promotion of the dimensionality reduction modeling and multistability reconstitution are proceeded, and the application prospect is prospected by taking the synchronization application of the memristor-coupled system as an example.

Memristors as Candidates for Replacing Digital Potentiometers in Electric Circuits

Digital potentiometers are substantial components for the design of many mixed-signal electronic circuits and systems. Their capability to program resistance value almost instantly provides hardware designers an additional level of freedom. Unfortunately, this feature is limited to DC and lower frequencies, due to parasitic effects. Nowadays, memristors as continuously tunable resistors are becoming candidates for potentiometer successors. Memristors are two-terminal non-volatile devices which have less significant parasitic effects and a wide resistance range. The memristance value can be changed on the fly. Using nanotechnology, memristor implementation has a nanoscale footprint with nanosecond transition between resistive states. In this paper, we present a comparison between the frequency characteristics of digital potentiometers and the only commercially available memristors. Memristor parasitic effects dominate at higher frequencies which extends the bandwidth. In order to present the advantages of memristive circuits, we have analyzed and implemented tunable circuits such as a voltage divider, an inverting amplifier, a high-pass filter, and a phase shifter. A commercially available memristor by KnowM Inc. is used for this purpose. Experimental results obtained by the measurements verify that a memristor has equal or better characteristics than a digital potentiometer. Memristive realizations of voltage dividers and inverting amplifiers have a wider bandwidth, while filters and phase shifters with a memristor have almost identical frequency characteristics as the corresponding realizations with a digital potentiometer.