Memristive Networks Research Articles

Synchronization and chimeras in asymmetrically coupled memristive Tabu learning neuron network

The coupling between neuronal oscillators plays an intriguing role in understanding the dynamics of the biological neurons present in realistic situations. Importantly, when the coupling between these neurons assumes an asymmetric nature, it can lead to profound changes in their overall behavior. In order to explore the impact of asymmetrical coupling on neuron models subjected to magnetic flux induction, we employ a coupled Tabu learning neuron model. Specifically, we illustrate the interplay between flux coupling and asymmetric electrical synapses concerning the control parameters of the proposed system using phase portraits, time series, bifurcation analysis, and Lyapunov spectrum. In particular, we show the dynamics by taking into account asymmetric interactions between neurons, from a simple network of two coupled systems to a network of nodes. Primarily, we demonstrate that two coupled systems exhibit synchronization for a fixed magnitude of control parameter with increasing coupling strength. Furthermore, we discuss the collective dynamics for the distinct network connectivity including regular, small-world and random. For all network connections, an increase in coupling strength facilitates a transition from desynchronization to synchronization via chimera state. We believe that attaining synchronization in Tabu learning neuron can act as a pivotal factor for neuron activity, contributing to the realization of such behavior in the context of numerous cognitive processes.

MODELIZACIÓN COMPUTACIONAL DE REDES MEMRISTORES: INFLUENCIA DELA CONECTIVIDAD Y LAS CONDICIONES AMBIENTALES EN SU RESPUESTAELÉCTRICACO

With the perspective of implementing neuromorphic devices using memristor networks, we present a numerical-computational platform that allows studying their electrical transport properties. It consists of a function that describes the behavior of an individual memristor (which enables the consideration of an experimental case of interest) and a connection diagram between memristors. Using this platform, two-dimensional networks of various sizes are studied,also incorporating environmental effects (such as humidity and temperature). Furthermore, by selecting the electrically accessible ports, the impact of connectivity on the electrical properties of the network is evaluated. The results indicate that, beyond the individual characteristics of the memristors (determined by the particular selected model), the degree of connectivity, the topology of the connections, and the environmental conditions significantly influence the macroscopic electrical response of the networks.

Deep brain stimulation and lag synchronization in a memristive two-neuron network

In the pursuit of potential treatments for neurological disorders and the alleviation of patient suffering, deep brain stimulation (DBS) has been utilized to intervene or investigate pathological neural activities. To explore the exact mechanism of how DBS works, a memristive two-neuron network considering DBS is newly proposed in this work. This network is implemented by coupling two-dimensional Morris–Lecar neuron models and using a memristor synaptic synapse to mimic synaptic plasticity. The complex bursting activities and dynamical effects are revealed numerically through dynamical analysis. By examining the synchronous behavior, the desynchronization mechanism of the memristor synapse is uncovered. The study demonstrates that synaptic connections lead to the appearance of time-lagged or asynchrony in completely synchronized firing activities. Additionally, the memristive two-neuron network is implemented in hardware based on FPGA, and experimental results confirm the abundant neuronal electrical activities and chaotic dynamical behaviors. This work offers insights into the potential mechanisms of DBS intervention in neural networks.

Designing Efficient Bit-Level Sparsity-Tolerant Memristive Networks.

With the rapid progress of deep neural network (DNN) applications on memristive platforms, there has been a growing interest in the acceleration and compression of memristive networks. As an emerging model optimization technique for memristive platforms, bit-level sparsity training (with the fixed-point quantization) can significantly reduce the demand for analog-to-digital converters (ADCs) resolution, which is critical for energy and area consumption. However, the bit sparsity and the fixed-point quantization will inevitably lead to a large performance loss. Different from the existing training and optimization techniques, this work attempts to explore more sparsity-tolerant architectures to compensate for performance degradation. We first empirically demonstrate that in a certain search space (e.g., 4-bit quantized DARTS space), network architectures differ in bit-level sparsity tolerance. It is reasonable and necessary to search the architectures for efficient deployment on memristive platforms by the neural architecture search (NAS) technology. We further introduce bit-level sparsity-tolerant NAS (BST-NAS), which encapsulates low-precision quantization and bit-level sparsity training into the differentiable NAS, to explore the optimal bit-level sparsity-tolerant architectures. Experimentally, with the same degree of sparsity and experiment settings, our searched architectures obtain a promising performance, which outperform the normal NAS-based DARTS-series architectures (about 5.8% higher than that of DARTS-V2 and 2.7% higher than that of PC-DARTS) on CIFAR10.

Chaos, synchronization, and emergent behaviors in memristive hopfield networks: bi-neuron and regular topology analysis

Chaos, synchronization, and emergent behaviors in memristive hopfield networks: bi-neuron and regular topology analysis

Modeling Excitable Cells with Memristors

This paper presents an in-depth analysis of an excitable membrane of a biological system by proposing a novel approach that the cells of the excitable membrane can be modeled as the networks of memristors. We provide compelling evidence from the Chay neuron model that the state-independent mixed ion channel is a nonlinear resistor, while the state-dependent voltage-sensitive potassium ion channel and calcium-sensitive potassium ion channel function as generic memristors from the perspective of electrical circuit theory. The mechanisms that give rise to periodic oscillation, aperiodic (chaotic) oscillation, spikes, and bursting in an excitable cell are also analyzed via a small-signal model, a pole-zero diagram of admittance functions, local activity, the edge of chaos, and the Hopf bifurcation theorem. It is also proved that the zeros of the admittance functions are equivalent to the eigen values of the Jacobian matrix, and the presence of the positive real parts of the eigen values between the two bifurcation points lead to the generation of complicated electrical signals in an excitable membrane. The innovative concepts outlined in this paper pave the way for a deeper understanding of the dynamic behavior of excitable cells, offering potent tools for simulating and exploring the fundamental characteristics of biological neurons.

Probability‐guaranteed encoding–decoding‐based state estimation for delayed memristive neutral networks with event‐triggered mechanism

SummaryThis article handles the probability‐guaranteed state estimation problem for a class of nonlinear memristive neural networks (MNNs) by using an event‐triggered mechanism. Both time‐varying delays and incomplete measurements are considered in the MNNs dynamics. To mitigate the impact of limited communication bandwidth, a communication protocol is proposed that incorporates an encoding–decoding technique in addition to an event‐triggered scheme. The aim is to devise a state estimator that can estimate the states of MNNs, ensuring that the state estimation error falls within the required ellipsoidal area with a desired chance. We obtain sufficient conditions for the feasibility of the addressed problem, where the requested gains can be found iteratively by solving certain convex optimization problems. On the basis of the proposed framework, some issues are further presented to determine locally optimal estimator parameters according to different specifications. Finally, we utilize an illustrative numerical example to show the validity of our provided theoretical results.

Coexisting firing patterns and attractor selection in memristive synapse coupled heterogeneous neurons

In this paper, we present a novel heterogeneous neuron network involving the coupling of a two-dimensional (2D) continuous Rulkov model with a 2D Hindmarsh-Rose (HR) neuron via memristive synapse. The present memristive coupled neuron network can produce an infinite number of coexisting hidden attractors with the same shape but located at different positions in the phase space, resulting in the interesting phenomenon of hidden homogeneous extreme multistability. Firstly, we study complex dynamical behaviors in detail through bifurcation diagrams, Lyapunov exponents, time series and phase portraits. Secondly, to select the desired firing pattern, a control method based on the feedback term is applied to the model. It is observed that the addition of this space-dependent feedback term to the dynamic equation of this model effectively eliminates all undesired firing patterns among the coexisting ones, and drives the heterogeneous neuron network to transition from coexisting hidden firing patterns to the expected firing pattern. Finally, Multisim circuit simulation is performed and the results are in line with numerical simulation.

Enabling reliable two-terminal memristor network by exploiting the dynamic reverse recovery in a diode selector

Enabling reliable two-terminal memristor network by exploiting the dynamic reverse recovery in a diode selector

Fractional-order heterogeneous memristive Rulkov neuronal network and its medical image watermarking application

This article proposes a novel fractional heterogeneous neural network by coupling a Rulkov neuron with a Hopfield neural network (FRHNN), utilizing memristors for emulating neural synapses. The study firstly demonstrates the coexistence of multiple firing patterns through phase diagrams, Lyapunov exponents (LEs), and bifurcation diagrams. Secondly, the parameter related firing behaviors are described through two-parameter bifurcation diagrams. Subsequently, local attraction basins reveal multi-stability phenomena related to initial values. Moreover, the proposed model is implemented on a microcomputer-based ARM platform, and the experimental results correspond to the numerical simulations. Finally, the article explores the application of digital watermarking for medical images, illustrating its features of excellent imperceptibility, extensive key space, and robustness against attacks including noise and cropping.

Ergodicity, lack thereof, and the performance of reservoir computing with memristive networks

Networks composed of nanoscale memristive components, such as nanowire and nanoparticle networks, have recently received considerable attention because of their potential use as neuromorphic devices. In this study, we explore ergodicity in memristive networks, showing that the performance on machine leaning tasks improves when these networks are tuned to operate at the edge between two global stability points. We find this lack of ergodicity is associated with the emergence of memory in the system. We measure the level of ergodicity using the Thirumalai-Mountain metric, and we show that in the absence of ergodicity, two different memristive network systems show improved performance when utilized as reservoir computers (RC). We highlight that it is also important to let the system synchronize to the input signal in order for the performance of the RC to exhibit improvements over the baseline.

The design of self-healing memristive network circuit based on VTA DA neurons and its application

This paper proposes a self-healing memristive network circuit, which simulates the resilience mechanism of VTA DA neurons. The proposed memristive network circuit mainly consists of four modules: input (synapse) module, damage detection module, threshold trigger module and negative feedback module. The input module is composed of a memristive synaptic circuit, which can react to a harmful initial input rather than a normal initial input. Apart from reacting to initial input, the input module also can receive a feedback signal released by the negative feedback module, and the process of receiving feedback signal is the key of realizing the self-healing function. The damage detection module can output a low level pulse that acts as an input signal of the threshold trigger module when the harmful initial input exists. The threshold trigger module will activate the negative feedback module when the trigger point which corresponds to the positive threshold voltage of memristor is reached. As the last module of the self-healing function, the negative feedback module can transmit the feedback signal, also be called a repairing signal, to the damaged memristor of the input module. The PSPICE simulation results indicate that the proposed memristive network circuit can realize the self-healing function which corresponds to the resilience mechanism of the VTA DA neurons. Meanwhile, when the proposed memristive network circuit has been applied to the damaged electronic machines or robots, the self-healing function of it can make the machines be reusable.

Affective computing for human-machine interaction via a bionic organic memristor exhibiting selective in situ activation.

Affective computing, representing the forefront of human-machine interaction, is confronted with the pressing challenges of the execution speed and power consumption brought by the transmission of massive data. Herein, we introduce a bionic organic memristor inspired by the ligand-gated ion channels (LGICs) to facilitate near-sensor affective computing based on electroencephalography (EEG). It is constructed from a coordination polymer comprising Co ions and benzothiadiazole (Co-BTA), featuring multiple switching sites for redox reactions. Through advanced characterizations and theoretical calculations, we demonstrate that when subjected to a bias voltage, only the site where Co ions bind with N atoms from four BTA molecules becomes activated, while others remain inert. This remarkable phenomenon resembles the selective in situ activation of LGICs on the postsynaptic membrane for neural signal regulation. Consequently, the bionic organic memristor network exhibits outstanding reliability (200 000 cycles), exceptional integration level (210 pixels), ultra-low energy consumption (4.05 pJ), and fast switching speed (94 ns). Moreover, the built near-sensor system based on it achieves emotion recognition with an accuracy exceeding 95%. This research substantively adds to the ambition of realizing empathetic interaction and presents an appealing bionic approach for the development of novel electronic devices.

EMSN: An Energy-Efficient Memristive Sequencer Network for Human Emotion Classification in Mental Health Monitoring

Mental health problems are an increasingly common social issue severely affecting health and well-being. Multimedia processing technologies via facial expression show appealing prospects in the consumer field for mental health monitoring, while still suffer from intensive computation and low energy efficiency. This paper proposes an energy-efficiency memristive sequencer network (EMSN) for human emotion classification, which offers an environmentally friendly approach for consumers with low cost and easily deployable hardware. Firstly, two-dimensional (2D) materials are employed to construct an eco-friendly memristor, the efficacy and reliability of which are confirmed through performance testing. Then, a sequencer block is proposed using memristive circuits. Notably, it is a core component of the EMSN, consisting of a bidirectional long short-term memory circuit, normalisation circuit module, and multi-layer perception module. After combining some necessary function modules, the EMSN can be achieved. Furthermore, the proposed EMSN is applied for human emotion classification. The experimental results demonstrate that the proposed EMSN has advantages in computational efficiency and classification accuracy compared to existing mainstream methods, indicating an advancement in consumer health monitoring.

Generative complex networks within a dynamic memristor with intrinsic variability

Artificial neural networks (ANNs) have gained considerable momentum in the past decade. Although at first the main task of the ANN paradigm was to tune the connection weights in fixed-architecture networks, there has recently been growing interest in evolving network architectures toward the goal of creating artificial general intelligence. Lagging behind this trend, current ANN hardware struggles for a balance between flexibility and efficiency but cannot achieve both. Here, we report on a novel approach for the on-demand generation of complex networks within a single memristor where multiple virtual nodes are created by time multiplexing and the non-trivial topological features, such as small-worldness, are generated by exploiting device dynamics with intrinsic cycle-to-cycle variability. When used for reservoir computing, memristive complex networks can achieve a noticeable increase in memory capacity a and respectable performance boost compared to conventional reservoirs trivially implemented as fully connected networks. This work expands the functionality of memristors for ANN computing.

A multiplier-free Rulkov neuron under memristive electromagnetic induction: Dynamics analysis, energy calculation, and circuit implementation

Establishing a realistic and multiplier-free implemented biological neuron model is significant for recognizing and understanding natural firing behaviors, as well as advancing the integration of neuromorphic circuits. Importantly, memristors play a crucial role in constructing memristive neuron and network models by simulating synapses or electromagnetic induction. However, existing models lack the consideration of initial-boosted extreme multistability and its associated energy analysis. To this end, we propose a multiplier-free implementation of the Rulkov neuron model and utilize a periodic memristor to represent the electromagnetic induction effect, thereby achieving the biomimetic modeling of the non-autonomous memristive Rulkov (mRulkov) neuron. First, theoretical analysis demonstrates that the stability distribution of the time-varying line equilibrium point is determined by both the parameters and the memristor’s initial condition. Furthermore, numerical simulations show that the mRulkov neuron can exhibit parameter-dependent local spiking, local hidden spiking, and periodic bursting firing behaviors. In addition, based on the periodic characteristics of the memductance function, the topological invariance of the mRulkov neuron is comprehensively proved. Therefore, local basins of attraction, bifurcation diagrams, and attractors related to extreme multistability can be boosted by switching the memristor’s initial condition. Significantly, the novel boosted extreme multistability is discovered in the Rulkov neuron for the first time. More importantly, the energy transition associated with the boosting dynamics is revealed through computing the Hamilton energy distribution. Finally, we develop a simulation circuit for the non-autonomous mRulkov neuron and confirm the effectiveness of the multiplier-free implementation and the accuracy of the numerical results through PSpice simulations.

Deep reservoir computing based on self-rectifying memristor synapse for time series prediction

Herein, a self-rectifying resistive switching memristor synapse with a Ta/NbOx/Pt structure was demonstrated for deep reservoir computing (RC). The memristor demonstrated stable nonlinear analog switching characteristics, with a rectification ratio of up to 1.6 × 105, good endurance, and high uniformity. Additionally, the memristor exhibited typical short-term plasticity and dynamic synaptic characteristics. Based on these characteristics, a deep memristor RC system was proposed for time series prediction. The system achieved a low normalized root mean square error (NRMSE) of 0.04 in the time series prediction of the Henon map. Even at 90 °C, deep RC retains good predictive power with an NRMSE of only 0.07. This work provides guidance for efficient deep memristive RC networks to handle more complex future temporal tasks.

Conduction and entropy analysis of a mixed memristor-resistor model for neuromorphic networks

To build neuromorphic hardware with self-assembled memristive networks, it is necessary to determine how the functional connectivity between electrodes can be adjusted, under the application of external signals. In this work, we analyse a model of a disordered memristor-resistor network, within the framework of graph theory. Such a model is well suited for the simulation of physical self-assembled neuromorphic materials where impurities are likely to be present. Two primary mechanisms that modulate the collective dynamics are investigated: the strength of interaction, i.e. the ratio of the two limiting conductance states of the memristive components, and the role of disorder in the form of density of Ohmic conductors (OCs) diluting the network. We consider the case where a fraction of the network edges has memristive properties, while the remaining part shows pure Ohmic behaviour. We consider both the case of poor and good OCs. Both the role of the interaction strength and the presence of OCs are investigated in relation to the trace formation between electrodes at the fixed point of the dynamics. The latter is analysed through an ideal observer approach. Thus, network entropy is used to understand the self-reinforcing and cooperative inhibition of other memristive elements resulting in the formation of a winner-take-all path. Both the low interaction strength and the dilution of the memristive fraction in a network provide a reduction of the steep non-linearity in the network conductance under the application of a steady input voltage. Entropy analysis shows enhanced robustness in selective trace formation to the applied voltage for heterogeneous networks of memristors diluted by poor OCs in the vicinity of the percolation threshold. The input voltage controls the diversity in trace formation.

Self-Organized Memristive Ensembles of Nanoparticles Below the Percolation Threshold: Switching Dynamics and Phase Field Description.

Percolative memristive networks based on self-organized ensembles of silver and gold nanoparticles are synthesized and investigated. Using cyclic voltammetry, pulse and step voltage excitations, we study switching between memristive and capacitive states below the percolation threshold. The resulting systems demonstrate scale-free (self-similar) temporal dynamics, long-term correlations, and synaptic plasticity. The observed plasticity can be manipulated in a controlled manner. The simplified stochastic model of resistance dynamics in memristive networks is testified. A phase field model based on the Cahn-Hilliard and Ginzburg-Landau equations is proposed to describe the dynamics of a self-organized network during the dissolution of filaments.

Synchronization and patterns in a memristive network in noisy electric field

Synchronization and patterns in a memristive network in noisy electric field