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

Stability analysis for delayed quaternion-valued neural networks via nonlinear measure approach

In this paper, the existence and stability analysis of the quaternion-valued neural networks (QVNNs) with time delay are considered. Firstly, the QVNNs are equivalently transformed into four real-valued systems. Then, based on the Lyapunov theory, nonlinear measure approach, and inequality technique, some sufficient criteria are derived to ensure the existence and uniqueness of the equilibrium point as well as global stability of delayed QVNNs. In addition, the provided criteria are presented in the form of linear matrix inequality (LMI), which can be easily checked by LMI toolbox in MATLAB. Finally, two simulation examples are demonstrated to verify the effectiveness of obtained results. Moreover, the less conservatism of the obtained results is also showed by two comparison examples

Exponential Lag Synchronization of Cohen-Grossberg Neural Networks with Discrete and Distributed Delays on Time Scales

In this article, we investigate exponential lag synchronization results for the Cohen-Grossberg neural networks (C-GNNs) with discrete and distributed delays on an arbitrary time domain by applying feedback control. We formulate the problem by using the time scales theory so that the results can be applied to any uniform or non-uniform time domains. Also, we provide a comparison of results that shows that obtained results are unified and generalize the existing results. Mainly, we use the unified matrix-measure theory and Halanay inequality to establish these results. In the last section, we provide two simulated examples for different time domains to show the effectiveness and generality of the obtained analytical results.Comment: 20 pages, 18 figure

Dynamics and Synchronization in Neuronal Models

La tesis está principalmente dedicada al modelado y simulación de sistemas neuronales. Entre otros aspectos se investiga el papel del ruido cuando actua sobre neuronas. El fenómeno de resonancia estocástica es caracterizado tanto a nivel teórico como reportado experimentalmente en un conjunto de neuronas del sistema motor. También se estudia el papel que juega la heterogeneidad en un conjunto de neuronas acopladas demostrando que la heterogeneidad en algunos parámetros de las neuronas puede mejorar la respuesta del sistema a una modulación periódica externa. También estudiamos del efecto de la topología y el retraso en las conexiones en una red neuronal. Se explora como las propiedades topológicas y los retrasos en la conducción de diferentes clases de redes afectan la capacidad de las neuronas para establecer una relación temporal bien definida mediante sus potenciales de acción. En particular, el concepto de consistencia se introduce y estudia en una red neuronal cuando plasticidad neuronal es tenida en cuenta entre las conexiones de la re

Multi-weighted complex structure on fractional order coupled neural networks with linear coupling delay: a robust synchronization problem

This sequel is concerned with the analysis of robust synchronization for a multi-weighted complex structure on fractional-order coupled neural networks (MWCFCNNs) with linear coupling delays via state feedback controller. Firstly, by means of fractional order comparison principle, suitable Lyapunov method, Kronecker product technique, some famous inequality techniques about fractional order calculus and the basis of interval parameter method, two improved robust asymptotical synchronization analysis, both algebraic method and LMI method, respectively are established via state feedback controller. Secondly, when the parameter uncertainties are ignored, several synchronization criterion are also given to ensure the global asymptotical synchronization of considered MWCFCNNs. Moreover, two type of special cases for global asymptotical synchronization MWCFCNNs with and without linear coupling delays, respectively are investigated. Ultimately, the accuracy and feasibility of obtained synchronization criteria are supported by the given two numerical computer simulations.This article has been written with the joint financial support of RUSA-Phase 2.0 grant sanctioned vide letter No.F 24-51/2014-U, Policy (TN Multi-Gen), Dept. of Edn. Govt. of India, UGC-SAP (DRS-I) vide letter No.F.510/8/DRSI/2016(SAP-I) and DST (FIST - level I) 657876570 vide letter No.SR/FIST/MS-I/2018/17

Synchrony, metastability, dynamic integration, and competition in the spontaneous functional connectivity of the human brain

Available online 3 June 2019.The human brain is functionally organized into large-scale neural networks that are dynamically interconnected. Multiple short-lived states of resting-state functional connectivity (rsFC) identified transiently synchronized networks and cross-network integration. However, little is known about the way brain couplings covary as rsFC states wax and wane. In this magnetoencephalography study, we explore the synchronization structure among the spontaneous interactions of well-known resting-state networks (RSNs). To do so, we extracted modes of dynamic coupling that reflect rsFC synchrony and analyzed their spatio-temporal features. These modes identified transient, sporadic rsFC changes characterized by the widespread integration of RSNs across the brain, most prominently in the β band. This is in line with the metastable rsFC state model of resting-state dynamics, wherein our modes fit as state transition processes. Furthermore, the default-mode network (DMN) stood out as being structured into competitive cross-network couplings with widespread DMN-RSN interactions, especially among the β-band modes. These results substantiate the theory that the DMN is a core network enabling dynamic global brain integration in the β band.This work was supported by the Action de Recherche Concert ee (ARC Consolidation 2015–2019, “Characterization of the electrophysiological bases, the temporal dynamics and the functional relevance of resting state network” attributed to X.D.T.) and by the research convention “Les Voies du Savoir” (Fonds Erasme, Brussels, Belgium). M.B. benefited from the program Attract of Innoviris (grant 2015-BB2B-10), the Spanish Ministry of Economy and Competitiveness (grant PSI2016-77175-P), and theMarie Skłodowska-Curie Action of the European Commission (grant 743562). M.V.G. and G.N.were supported by the Fonds Erasme. N.C. benefited from a research grant from the ARC Consolidation (2014–2017, “Characterization of the electrophysiological bases, the temporal dynamics and the functional relevance of resting state network” attributed to X.D.T.) and from the Fonds Erasme (research convention “Les Voies du Savoir”). X.D.T. is Post-doctorate Clinical Master Specialist at the Fonds de la Recherche Scientifique (F.R.S.-FNRS, Brussels, Belgium). The MEG project at the CUB – H^opital Erasme is financially supported by the Fonds Erasme (research convention “Les Voies du Savoir”)