On Local Activity and Edge of Chaos in a NaMLab Memristor

Abstract

Local activity is the capability of a system to amplify infinitesimal fluctuations in energy. Complex phenomena, including the generation of action potentials in neuronal axon membranes, may never emerge in an open system unless some of its constitutive elements operate in a locally active regime. As a result, the recent discovery of solid-state volatile memory devices, which, biased through appropriate DC sources, may enter a local activity domain, and, most importantly, the associated stable yet excitable sub-domain, referred to as edge of chaos, which is where the seed of complexity is actually planted, is of great appeal to the neuromorphic engineering community. This paper applies fundamentals from the theory of local activity to an accurate model of a niobium oxide volatile resistance switching memory to derive the conditions necessary to bias the device in the local activity regime. This allows to partition the entire design parameter space into three domains, where the threshold switch is locally passive (LP), locally active but unstable, and both locally active and stable, respectively. The final part of the article is devoted to point out the extent by which the response of the volatile memristor to quasi-static excitations may differ from its dynamics under DC stress. Reporting experimental measurements, which validate the theoretical predictions, this work clearly demonstrates how invaluable is non-linear system theory for the acquirement of a comprehensive picture of the dynamics of highly non-linear devices, which is an essential prerequisite for a conscious and systematic approach to the design of robust neuromorphic electronics. Given that, as recently proved, the potassium and sodium ion channels in biological axon membranes are locally active memristors, the physical realization of novel artificial neural networks, capable to reproduce the functionalities of the human brain more closely than state-of-the-art purely CMOS hardware architectures, should not leave aside the adoption of resistance switching memories, which, under the appropriate provision of energy, are capable to amplify the small signal, such as the niobium dioxide micro-scale device from NaMLab, chosen as object of theoretical and experimental study in this work.

Chemical Inductor

“…In the paper of HH, the neuron-equivalent circuit is presented in terms of time-dependent resistances, as shown in Figure a, and the inductor does not appear explicitly. However, whenever the small ac impedance of the HH model is calculated, ,,− a circuit of the classes of Figure b–d appears, and this is because HH contains the mechanism of the chemical inductor. Early measurements of the neuron impedance are shown in Figure , providing a clear instance of the chemical inductor in an oscillating system.…”

Mutual Transformation of Flux-Controlled and Charge-Controlled Memristors

“…The memristors with non-monotonic constitutive relations can be easily implemented as popular and in the literature well described memristors with piece-wise-linear characteristics [3], [13]. Such locally active memristors can be useful for constructing nonlinear oscillators, artificial neurons, and networks working on the edge of chaos [14], [15], while passive memristors are useful for mimicking the synapses [16]. Emulators of the active memristors are used in this work for generating nonlinear oscillations via two benchmark circuits, denoted above as the applications App1 and App2.…”

Hardware Implementation of Differential Oscillatory Neural Networks Using VO 2-Based Oscillators and Memristor-Bridge Circuits

“…A memristor is a two-terminal resistive device whose resistance is adjustable. It is typically used as an analog memory that can be both non-volatile or volatile (Ohno et al, 2011;van den Hurk et al, 2014;La Barbera et al, 2015;Wang et al, 2017;Ascoli et al, 2021). In addition, the adjustability of non-volatile memristors and their nanoscale size make them attractive candidates to implement massive adjustable synaptic circuits, especially with crossbar structures.…”