Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules

This paper presents theoretical results on the multistability and fixed-time synchronization of switched neural networks with multiple almost-periodic solutions and state-dependent switching rules. It is shown herein that the number, location, and stability of the almost-periodic solutions of the switched neural networks can be characterized by making use of the state-space partition. Two sets of sufficient conditions are derived to ascertain the existence of 3n exponentially stable almost-periodic solutions. Subsequently, this paper introduces the novel concept of fixed-time multisynchronization in switched neural networks associated with a range of almost-periodic parameters within multiple stable equilibrium states for the first time. Based on the multistability results, it is demonstrated that there are 3n synchronization manifolds, wherein n is the number of neurons. Additionally, an estimation for the settling time required for drive-response switched neural networks to achieve synchronization is provided. It should be noted that this paper considers stable equilibrium points (static multisynchronization), stable almost-periodic orbits (dynamical multisynchronization), and hybrid stable equilibrium states (hybrid multisynchronization) as special cases of multistability (multisynchronization). Two numerical examples are elaborated to substantiate the theoretical results.

Memristive competitive hopfield neural network for image segmentation application

Image segmentation implementation provides simplified and effective feature information of image. Neural network algorithms have made significant progress in the application of image segmentation task. However, few studies focus on the implementation of hardware circuits with high-efficiency analog calculations and parallel operations for image segmentation problem. In this paper, a memristor-based competitive Hopfield neural network circuit is proposed to deal with the image segmentation problem. In this circuit, the memristive cross array is applied to store synaptic weights and perform matrix operations. The competition module based on the Winner-take-all mechanism is composed of the competition neurons and the competition control circuit, which simplifies the energy function of the Hopfield neural network and realizes the output function. Operational amplifiers and ABM modules are used to integrate operations and process external input information, respectively. Based on these designs, the circuit can automatically implement iteration and update of data. A series of PSPICE simulations are designed to verify the image segmentation capability of this circuit. Comparative experimental results and analysis show that this circuit has effective improvements both in processing speed and segmentation accuracy compared with other methods. Moreover, the proposed circuit shows good robustness to noise and memristive variation.

Event-triggered control for robust exponential synchronization of inertial memristive neural networks under parameter disturbance

Synchronization of memristive neural networks (MNNs) by using network control scheme has been widely and deeply studied. However, these researches are usually restricted to traditional continuous-time control methods for synchronization of the first-order MNNs. In this paper, we study the robust exponential synchronization of inertial memristive neural networks (IMNNs) with time-varying delays and parameter disturbance via event-triggered control (ETC) scheme. First, the delayed IMNNs with parameter disturbance are changed into first-order MNNs with parameter disturbance by constructing proper variable substitutions. Next, a kind of state feedback controller is designed to the response IMNN with parameter disturbance. Based on feedback controller, some ETC methods are provided to largely decrease the update times of controller. Then, some sufficient conditions are provided to realize robust exponential synchronization of delayed IMNNs with parameter disturbance via ETC scheme. Moreover, the Zeno behavior will not happen in all ETC conditions shown in this paper. Finally, numerical simulations are given to verify the advantages of the obtained results such as anti-interference performance and good reliability.

Offset parameter cancellation produces countless coexisting attractors

The average value of a system variable determines the position of its attractor. When the offset parameters come together and get disappeared after an algebraic operation, the location of the attractor is then governed by an initial condition only. In this case, parameter-dominated offset control turns out to be the initial condition-defined coexisting attractors. In this Letter, a special mechanism for generating countless coexisting attractors is disclosed. Furthermore, a new regime of multistability is revealed, which explains where and how countless coexisting attractors are born and arranged.

Rulkov neural network coupled with discrete memristors

The features of memristive-coupled neural networks have been studied extensively in the continuous field. However, the particularities of the discrete domain are rarely mentioned. This paper constructs a discrete memristor with sine-type conductance and applies the discrete memristor to coupling the Rulkov neuron maps for the first time. The properties of the proposed memristive-coupled bi-neuron Rulkov map and multi-neuron Rulkov neural network are probed. In order to better characterize the discrete system, many numerical simulation methods are used. Such as the normalized mean synchronization error, bifurcation diagrams, phase portraits, spatiotemporal patterns and so on. Numerical studies have shown that in discrete memristor-coupled neural networks, both parameters and coupling factors affect the dynamics of the system, resulting in complex and interesting behavioural changes.

Convergence of a Class of Delayed Neural Networks with Real Memristor Devices

Neural networks with memristors are promising candidates to overcome the limitations of traditional von Neumann machines via the implementation of novel analog and parallel computation schemes based on the in-memory computing principle. Of special importance are neural networks with generic or extended memristor models that are suited to accurately describe real memristor devices. The manuscript considers a general class of delayed neural networks where the memristors obey the relevant and widely used generic memristor model, the voltage threshold adaptive memristor (VTEAM) model. Due to physical limitations, the memristor state variables evolve in a closed compact subset of the space; therefore, the network can be mathematically described by a special class of differential inclusions named differential variational inequalities (DVIs). By using the theory of DVI, and the Lyapunov approach, the paper proves some fundamental results on convergence of solutions toward equilibrium points, a dynamic property that is extremely useful in neural network applications to content addressable memories and signal-processing in real time. The conditions for convergence, which hold in the general nonsymmetric case and for any constant delay, are given in the form of a linear matrix inequality (LMI) and can be readily checked numerically. To the authors knowledge, the obtained results are the only ones available in the literature on the convergence of neural networks with real generic memristors.

Memristive Circuit Implementation of a Self-Repairing Network Based on Biological Astrocytes in Robot Application

A large number of studies have shown that astrocytes can be combined with the presynaptic terminals and postsynaptic spines of neurons to constitute a triple synapse via an endocannabinoid retrograde messenger to achieve a self-repair ability in the human brain. Inspired by the biological self-repair mechanism of astrocytes, this work proposes a self-repairing neuron network circuit that utilizes a memristor to simulate changes in neurotransmitters when a set threshold is reached. The proposed circuit simulates an astrocyte-neuron network and comprises the following: 1) a single-astrocyte-neuron circuit module; 2) an astrocyte-neuron network circuit; 3) a module to detect malfunctions; and 4) a neuron PR (release probability of synaptic transmission) enhancement module. When faults occur in a synapse, the neuron module becomes silent or near silent because of the low PR of the synapses. The circuit can detect faults automatically. The damaged neuron can be repaired by enhancing the PR of other healthy neurons, analogous to the biological repair mechanism of astrocytes. This mechanism helps to repair the damaged circuit. A simulation of the circuit revealed the following: 1) as the number of neurons in the circuit increases, the self-repair ability strengthens and 2) as the number of damaged neurons in the astrocyte-neuron network increases, the self-repair ability weakens, and there is a significant degradation in the performance of the circuit. The self-repairing circuit was used for a robot, and it effectively improved the robots' performance and reliability.

Asymptotic Synchronization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delays via Event-Triggered Control Scheme

This paper investigates the asymptotic synchronization of memristive Cohen-Grossberg neural networks (MCGNNs) with time-varying delays under event-triggered control (ETC). First, based on the designed feedback controller, some ETC conditions are provided. It is demonstrated that ETC can significantly reduce the update times of the controller and decrease the computing cost. Next, some sufficient conditions are derived to ensure the asymptotic synchronization of MCGNNs with time-varying delays under the ETC method. Finally, a numerical example is provided to verify the correctness and effectiveness of the obtained results.

Dynamic analysis and application in medical digital image watermarking of a new multi-scroll neural network with quartic nonlinear memristor

Memristor is widely used in various neural bionic models because of its excellent characteristics in biological neural activity simulation. In this paper, a piecewise nonlinear function is used to transform the quartic memristor, which is introduced into the ternary Hopfield neural network (HNN) with self-feedback, and a piecewise quartic memristive chaotic neural network model with multi-scroll is constructed. Through simulation analysis, the number of scroll layers changes with memristor parameters and has significant coexistence of multi-scroll attractors and high initial value sensitivity has been found. Using its excellent unpredictability, a digital watermarking algorithm based on wavelet transform is improved and used in the protection of personal medical data. The results show that it not only improves the confidentiality and convenience, but also ensures its robustness and has good encryption effect.

Pinning multisynchronization of delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations

This paper concerns the multisynchronization issue for delayed fractional-order memristor-based neural networks with nonlinear coupling and almost-periodic perturbations. First, the coexistence of multiple equilibrium states for isolated subnetwork is analyzed. By means of state-space decomposition, fractional-order Halanay inequality and Caputo derivative properties, the novel algebraic sufficient conditions are derived to ensure that the addressed networks with arbitrary activation functions have multiple locally stable almost periodic orbits or equilibrium points. Then, based on the obtained multistability results, a pinning control strategy is designed to realize the multisynchronization of the N coupled networks. By the aid of graph theory, depth first search method and pinning control law, some sufficient conditions are formulated such that the considered neural networks can possess multiple synchronization manifolds. Finally, the multistability and multisynchronization performance of the considered neural networks with different activation functions are illustrated by numerical examples.

Dynamical and static multisynchronization analysis for coupled multistable memristive neural networks with hybrid control

This paper investigates the dynamical multisynchronization (DMS) and static multisynchronization (SMS) problems for a class of delayed coupled multistable memristive neural networks (DCMMNNs) via a novel hybrid controller which includes delayed impulsive control and state feedback control. Based on the state-space partition method and the geometrical properties of the activation function, each subnetwork has multiple locally exponential stable equilibrium states. By employing a new Halanay-type inequality and the impulsive control theory, some new linear matrix inequalities (LMIs)-based sufficient conditions are proposed. It is shown that the delayed impulsive control with suitable impulsive interval and allowable time-varying delay can still guarantee the DMS and SMS of DCMMNNs. Finally, a numerical example is presented to illustrate the effectiveness of the hybrid controller.

Memristive Circuit Implementation of Biological Nonassociative Learning Mechanism and Its Applications

Biological nonassociative learning is one of the simplest forms of unsupervised learning in animals and can be categorized into habituation and sensitization according to mechanism. This paper proposes a memristive circuit that is based on nonassociative learning and can adapt to repeated inputs, reduce power consumption (habituation), and be sensitive to harmful inputs (sensitization). The circuit includes 1) synapse module, 2) neuron module, 3) feedback module. The first module mainly consists of memristors representing synapse weights that vary with corresponding inputs. Memristance is automatically reduced when a harmful stimulus is input, and climbs at the input interval according to the feedback input when repeated stimuli are input. The second module produces spiking voltage when the total input is above the given threshold. The third module can provide feedback voltage according to the frequency and quantity of input stimuli. Simulation results show that the proposed circuit can generate output signals with biological nonassociative learning characteristics, with varying amplitudes depending on the characteristics of input signals. When the frequency and quantity of the input stimuli are high, the degree of habituation and sensitization intensifies. The proposed circuit has good robustness; can reduce the influence of noise, circuit parasitics and circuit aging during nonassociative learning; and simulate the afterimages caused by visual fatigue for application in automatic exposure compensation.

Dynamics editing based on offset boosting

Multistability in a dynamical system has attracted great attention recently for its complex and unexpected states. Since in most chaotic systems coexisting attractors reside in their own individual basin of attraction with a fractal structure, it becomes a challenge to choose correct initial conditions to obtain desired dynamics. Selecting typical dynamics as the basic components in a dynamical sequence and then arranging them in the phase space in a desired order make the multistability transparent and controllable in the domain of initial conditions; thereafter, one can identify an attractor according to its initial sequence. Dynamics editing provides an effective technique to select typical attractors under different system parameters to form a flexible sequence in the phase space, which shows great potential for chaos-based secure communications.

A simple locally active memristor and its application in HR neurons

This paper proposes a simple locally active memristor whose state equation only consists of linear terms and an easily implementable function and design for its circuit emulator. The effectiveness of the circuit emulator is validated using breadboard experiments and numerical simulations. The proposed circuit emulator has a simple structure, which not only reduces costs but also increases its application value. The power-off plot and DC V-I Loci verify that the memristor is nonvolatile and locally active, respectively. This locally active memristor exhibits low cost, easy physical implementation, and wide locally active region characteristics. Furthermore, a neural model composed of two 2D HR neurons based on the proposed locally active memristor is established. It is found that complicated firing behaviors occur only within the locally active region. A new phenomenon is also discovered that shows coexisting position symmetry for different attractors. The firing pattern transition is then observed via bifurcation analysis. The results of MATLAB simulations are verified from the hardware circuits.