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SUMMARY A number of resistive switching memories exhibit activation-based dynamical behavior, which makes them suitable for neuromorphic and programmable analog filtering applications. Because the Boundary Condition Memristor (BCM) model accounts for tunable activation thresholds only at the on and off boundary states, it is not quantitatively accurate in the description of these kinds of memristors and in the investigation of their circuit applications. This paper introduces the Generalized Boundary Condition Memristor (GBCM) model, preserving the features of the BCM model while allowing, further, an ad-hoc tuning of activation-based dynamics, which enables an appropriate modulation of the conditions under which memristors may operate as storage elements or data processors. A simple circuit implementation of the novel model is presented, and time-efficient simulations confirming the improvement in modeling accuracy over the BCM model are shown. As a proof-of-concept for the suitability of the GBCM model in the exploration of the full potential of memristors in neuromorphic circuits and programmable analog filters, this paper adopts it to model fundamental synaptic rules governing the mechanisms of learning in neural systems and to gain some insight into key issues in the design of a couple of filters. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we propose a whole class of memristor circuits. Each element from the class consists of the cascade connection between a static nonlinear two-port and a dynamic one-port. The class may be divided into two subclasses depending on the input variable (voltage or current). Within each of these subclasses, two further sets of memristor circuits may be distinguished according to which output voltage and current of the two-port represents one of the system states. The simplest memristor circuits make only use of purely passive elementary components from circuit theory, an absolute novelty in this field of research. Thus they are suitable circuit primers for the introduction of the topic of memristors to undergraduate students. A sample circuit is built using discrete devices and its memristive nature is validated experimentally. In case the one-port is purely passive, the proposed circuits feature volatile memristive behavior. Allowing active devices into the dynamic one-port, non-volatile dynamics may also emerge, as proved through concepts from the theory of nonlinear dynamics. Given the generality of the proposed class, the topology of the emulators may be adjusted so as to induce a large variety of dynamical behaviors, which may be exploited to accomplish new signal processing tasks, which conventional circuits are unable to perform. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

According to the axiomatic definition of the memristor from 1971, its properties are unambiguously determined by the memristance versus charge (or flux) map. The original model of the 'HP memristor' introduces this map via a linear function that represents this memristor as a variable resistor whose resistance is linearly dependent on the amount of charge flowing through. However, some analog applications require nonlinear, frequently exponential or logarithmic dependence of the resistance on an external controlling variable. The memristor with nonlinear memristance versus charge map is analyzed in the paper. The results are specified for the exponential type of this nonlinearity, which may be useful for future applications. Analytic formulae of the area of the pinched hysteresis loop of such a memristor are derived for harmonic excitation. It is also shown that the current flowing through such a memristor, which is driven by a voltage of arbitrary waveform, conforms to the Abel differential equation, and its closed-form solution is found. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]