Dynamical properties of electrical circuits with fully nonlinear memristors

We introduce an approach based on the Chapman-Kolmogorov equation to model heterogeneous stochastic circuits, namely, the circuits combining binary or multi-state stochastic memristive devices and continuum reactive components (capacitors and/or inductors). Such circuits are described in terms of occupation probabilities of memristive states that are functions of reactive variables. As an illustrative example, the series circuit of a binary memristor and capacitor is consider...

This paper presents in-depth analysis of the excitable membranes of a biological system. We rigorously prove from the Chay neuron model that the state dependent voltage-sensitive potassium ion-channel and calcium sensitive potassium ion-channel in excitable cells are in-fact generic memristors and state independent mixed sodium and calcium ion-channel is non-memristive (nonlinear resistor) element in the perspective of electrical circuit theory. The mechanism to give the rise...

The interest in memristors has risen due to their possible application both as memory units and as computational devices in combination with CMOS. This is in part due to their nonlinear dynamics, and a strong dependence on the circuit topology. We provide evidence that also purely memristive circuits can be employed for computational purposes. In the present paper we show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memrist...

We construct an exactly solvable circuit of interacting memristors and study its dynamics and fixed points. This simple circuit model interpolates between decoupled circuits of isolated memristors, and memristors in series, for which exact fixed points can be obtained. We introduce a Lyapunov functional that is found to be minimized along the non-equilibrium dynamics and which resembles a long-range Ising Hamiltonian with non-linear self-interactions. We use the Lyapunov func...

The aim of this work is to propose an alternative method for determining the condition of existence of "canard solutions" for three and four-dimensional singularly perturbed systems with only one fast variable in the folded saddle case. This method enables to state a unique generic condition for the existence of "canard solutions" for such three and four-dimensional singularly perturbed systems which is based on the stability of folded singularities of the normalized slow dyn...

Nonlinearity is a crucial characteristic for implementing hardware security primitives or neuromorphic computing systems. The main feature of all memristive devices is this nonlinear behavior observed in their current-voltage characteristics. To comprehend the nonlinear behavior, we have to understand the coexistence of resistive, capacitive, and inertia (virtual inductive) effects in these devices. These effects originate from corresponding physical and chemical processes in...

In the present report, we have investigated the effect of the low-frequency signal on nanoscale memristor device. The frequency is varied from 2 Hz to 10 Hz and the corresponding effect on the current-voltage characteristics, time domain state variable, charge-magnetic flux relation, memristance-charge relation, memristance-voltage characteristics and memristance-magnetic flux relation are studied. The results clearly suggested that the frequency of the input stimulus plays a...

The memristor, the recently discovered fundamental circuit element, is of great interest for neuromorphic computing, nonlinear electronics and computer memory. It is usually modelled either using Chua's equations, which lack material device properties, or using Strukov's phenomenological model (or models derived from it), which deviates from Chua's definitions due to the lack of a magnetic flux term. It is shown that by modelling the magnetostatics of the memory-holding ionic...

In pursuit of neuromorphic (brain-inspired) devices, memristors (memory-resistors) have emerged as promising candidates for emulating neuronal circuitry. Here we mathematically define a class of Simple Volatile Memristors (SVMs), which notably includes various fluidic iontronic devices that have recently garnered significant interest due to their unique quality of operating within the same medium as the brain. We show that symmetric SVMs produce non self-crossing current-volt...

Biological neuronal networks are characterized by nonlinear interactions and complex connectivity. Given the growing impetus to build neuromorphic computers, understanding physical devices that exhibit structures and functionalities similar to biological neural networks is an important step toward this goal. Self-organizing circuits of nanodevices are at the forefront of the research in neuromorphic computing, as their behavior mimics synaptic plasticity features of biologica...