System-Theoretic Methods for Designing Bio-Inspired Mem-Computing Memristor Cellular Nonlinear Networks

Abstract

The introduction of nano-memristors in electronics may allow to boost the performance of integrated circuits beyond the Moore era, especially in view of their extraordinary capability to process and store data in the very same physical volume. However, recurring to nonlinear system theory is absolutely necessary for the development of a systematic approach to memristive circuit design. In fact, the application of linear system-theoretic techniques is not suitable to explore thoroughly the rich dynamics of resistance switching memories, and designing circuits without a comprehensive picture of the nonlinear behaviour of these devices may lead to the realization of technical systems failing to operate as desired. Converting traditional circuits to memristive equivalents may require the adaptation of classical methods from nonlinear system theory. This paper extends the theory of time- and space-invariant standard cellular nonlinear networks with first-order processing elements for the case where a single non-volatile memristor is inserted in parallel to the capacitor in each cell. A novel nonlinear system-theoretic method allows to draw a comprehensive picture of the dynamical phenomena emerging in the memristive mem-computing array, beautifully illustrated in the so-called Primary Mosaic for the class of uncoupled memristor cellular nonlinear networks. Employing this new analysis tool it is possible to elucidate, with the support of illustrative examples, how to design variability-tolerant bio-inspired cellular nonlinear networks with second-order memristive cells for the execution of computing tasks or of memory operations. The capability of the class of memristor cellular nonlinear networks under focus to store and process information locally, without the need to insert additional memory units in each cell, may allow to increase considerably the spatial resolution of state-of-the-art purely CMOS sensor-processor arrays. This is of great appeal for edge computing applications, especially since the Internet-of-Things industry is currently calling for the realization of miniaturized, lightweight, low-power, and high-speed mem-computers with sensing capability on board.

Pattern Formation in a RD-MCNN with Locally Active Memristors

“…Consistent with the above-mentioned text, locally active memristors have already been utilized in the design and application of spiking neural cells demonstrating promising results [20], while prominent artificial neural network designs employing memristor crossbar arrays have been presented in several works [21]. Besides, the theory of memristor cellular nonlinear networks (MCNNs) has been comprehensively investigated in [22][23][24][25] and the formation of Turing patterns with reaction-diffusion MCNNs (RD-MCNNs) has been introduced in [26]. In addition, pattern formation utilizing locally active NbO memristors in an MCNN has been presented in [27].…”

Initial state‐dependent implementation of logic gates with memristive neurons

“…The subject of our investigation is a memristive cellular neural network (M-CellNN) [14] comprising two cells.…”

The State Change Per Cycle Map: a novel system-theoretic analysis tool for periodically-driven ReRAM cells

“…Furthermore, while densely packed across crossbar arrays, stacked on top of standard CMOS circuitry by exploiting the natural availability of metal-insulator-metal layers along the third dimension in IC fabrication processes, they allow efficient use of the available area, endowing the resulting hybrid hardware platforms with add-on capabilities as compared to conventional technical systems. For example, non-volatile memristors enable the processing elements of standard cellular dynamic arrays to perform memory operations without the need for additional data storage units (Ascoli et al, 2021b).Interestingly, memristors may do much more. Certain resistance switching memories (Ascoli et al, 2021a), unable to store data, are attracting an increasing interest in both academia and industry for their extraordinary capability to act as sources of infinitesimal energy under suitable polarization, analogous to the ion channels in biological neuronal membranes.…”