Finite-time Anti-synchronization of Memristive Stochastic BAM Neural Networks with Probabilistic Time-varying Delays

This paper investigates the drive-response finite-time anti-synchronization for memristive bidirectional associative memory neural networks (MBAMNNs). Firstly, a class of MBAMNNs with mixed probabilistic time-varying delays and stochastic perturbations is first formulated and analyzed in this paper. Secondly, an nonlinear control law is constructed and utilized to guarantee drive-response finite-time anti-synchronization of the neural networks. Thirdly, by employing some inequality technique and constructing an appropriate Lyapunov function, some anti-synchronization criteria are derived. Finally, a number simulation is provided to demonstrate the effectiveness of the proposed mechanism

Improved synchronization analysis of competitive neural networks with time-varying delays

Synchronization and control are two very important aspects of any dynamical systems. Among various kinds of nonlinear systems, competitive neural network holds a very important place due to its application in diverse fields. The model is general enough to include, as subclass, the most famous neural network models such as competitive neural networks, cellular neural networks and Hopfield neural networks. In this paper, the problem of feedback controller design to guarantee synchronization for competitive neural networks with time-varying delays is investigated. The goal of this work is to derive an existent criterion of the controller for the exponential synchronization between drive and response neutral-type competitive neural networks with time-varying delays. The method used in this brief is based on feedback control gain matrix by using the Lyapunov stability theory. The synchronization conditions are given in terms of LMIs. To the best of our knowledge, the results presented here are novel and generalize some previous results. Some numerical simulations are also represented graphically to validate the effectiveness and advantages of our theoretical results

Exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays via periodically intermittent control

This paper deals with the exponential synchronization problem for reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, a periodically intermittent controller is first proposed to guarantee the exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance in terms of p-norm. The obtained synchronization results are easy to check and improve upon the existing ones. Particularly, the traditional assumptions on control width and time-varying delays are removed in this paper. This paper also presents two illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme

The effect of heterogeneity on decorrelation mechanisms in spiking neural networks: a neuromorphic-hardware study

High-level brain function such as memory, classification or reasoning can be realized by means of recurrent networks of simplified model neurons. Analog neuromorphic hardware constitutes a fast and energy efficient substrate for the implementation of such neural computing architectures in technical applications and neuroscientific research. The functional performance of neural networks is often critically dependent on the level of correlations in the neural activity. In finite networks, correlations are typically inevitable due to shared presynaptic input. Recent theoretical studies have shown that inhibitory feedback, abundant in biological neural networks, can actively suppress these shared-input correlations and thereby enable neurons to fire nearly independently. For networks of spiking neurons, the decorrelating effect of inhibitory feedback has so far been explicitly demonstrated only for homogeneous networks of neurons with linear sub-threshold dynamics. Theory, however, suggests that the effect is a general phenomenon, present in any system with sufficient inhibitory feedback, irrespective of the details of the network structure or the neuronal and synaptic properties. Here, we investigate the effect of network heterogeneity on correlations in sparse, random networks of inhibitory neurons with non-linear, conductance-based synapses. Emulations of these networks on the analog neuromorphic hardware system Spikey allow us to test the efficiency of decorrelation by inhibitory feedback in the presence of hardware-specific heterogeneities. The configurability of the hardware substrate enables us to modulate the extent of heterogeneity in a systematic manner. We selectively study the effects of shared input and recurrent connections on correlations in membrane potentials and spike trains. Our results confirm ...Comment: 20 pages, 10 figures, supplement

Adaptive Exponential Synchronization for Stochastic Competitive Neural Networks with Time-Varying Leakage Delays and Reaction-Diffusion Terms

We study the exponential synchronization problem for a class of stochastic competitive neural networks with different timescales, as well as spatial diffusion, time-varying leakage delays, and discrete and distributed time-varying delays. By introducing several important inequalities and using Lyapunov functional technique, an adaptive feedback controller is designed to realize the exponential synchronization for the proposed competitive neural networks in terms of p-norm. According to the theoretical results obtained in this paper, the influences of the timescale, external stimulus constants, disposable scaling constants, and controller parameters on synchronization are analyzed. Numerical simulations are presented to show the feasibility of the theoretical results

Finite-time synchronisation of neural networks with discrete and distributed delays via periodically intermittent memory feedback control

In this paper, finite-time synchronization between two chaotic systems with discrete and distributed delays is investigated by using periodically intermittent memory feedback control. Based on finite-time stability theory, some novel and effective synchronization criteria of intermit- tent control are derived by means of linear matrix inequalities (LMIs) and differential inequality techniques. Furthermore, a necessary condition of finite-time synchronization of intermittent con- trol is given for neural networks with discrete and distributed delays. A numerical example on two chaotic neural networks shows the effectiveness and correctness of the derived theoretical results. In addition, a secure communication synchronization problem is presented to demonstrate practical effectiveness of the proposed method.National Natural Science Foundation of China (Grant No. 61273183, No. 61374028 and No. 61374085).http://www.ietdl.orgIET-CTAhb2016Electrical, Electronic and Computer Engineerin

Synchronization of Coupled and Periodically Forced Chemical Oscillators

Physiological rhythms are essential in all living organisms. Such rhythms are regulated through the interactions of many cells. Deviation of a biological system from its normal rhythms can lead to physiological maladies. The tremor and symptoms associated with Parkinson\u27s disease are thought to emerge from abnormal synchrony of neuronal activity within the neural network of the brain. Deep brain stimulation is a therapeutic technique that can remove this pathological synchronization by the application of a periodic desynchronizing signal. Herein, we used the photosensitive Belousov--Zhabotinsky (BZ) chemical reaction to test the mechanism of deep brain stimulation. A collection of oscillators are initially synchronized using a regular light signal. Desynchronization is then attempted using an appropriately chosen desynchronizing signal based on information found in the phase response curve.;Coupled oscillators in various network topologies form the most common prototypical systems for studying networks of dynamical elements. In the present study, we couple discrete BZ photochemical oscillators in a network configuration. Different behaviors are observed on varying the coupling strength and the frequency heterogeneity, including incoherent oscillations to partial and full frequency entrainment. Phase clusters are organized symmetrically or non-symmetrically in phase-lag synchronization structures, a novel phase wave entrainment behavior in non-continuous media. The behavior is observed over a range of moderate coupling strengths and a broad frequency distribution of the oscillators

Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

© 2021 IEEE - All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1109/TCSI.2021.3081150Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.Peer reviewe

Complex and Adaptive Dynamical Systems: A Primer

An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. It inludes chapter on Graph Theory and Small-World Networks, Chaos, Bifurcations and Diffusion, Complexity and Information Theory, Random Boolean Networks, Cellular Automata and Self-Organized Criticality, Darwinian evolution, Hypercycles and Game Theory, Synchronization Phenomena and Elements of Cognitive System Theory.Comment: unformatted version of the textbook; published in Springer, Complexity Series (2008, second edition 2010