Boundedness and stability for Cohen–Grossberg neural network with time-varying delays

AbstractIn this paper, a model is considered to describe the dynamics of Cohen–Grossberg neural network with variable coefficients and time-varying delays. Uniformly ultimate boundedness and uniform boundedness are studied for the model by utilizing the Hardy inequality. Combining with the Halanay inequality and the Lyapunov functional method, some new sufficient conditions are derived for the model to be globally exponentially stable. The activation functions are not assumed to be differentiable or strictly increasing. Moreover, no assumption on the symmetry of the connection matrices is necessary. These criteria are important in signal processing and the design of networks

Multi-almost periodicity and invariant basins of general neural networks under almost periodic stimuli

In this paper, we investigate convergence dynamics of $2^N$ almost periodic encoded patterns of general neural networks (GNNs) subjected to external almost periodic stimuli, including almost periodic delays. Invariant regions are established for the existence of $2^N$ almost periodic encoded patterns under two classes of activation functions. By employing the property of $\mathscr{M}$-cone and inequality technique, attracting basins are estimated and some criteria are derived for the networks to converge exponentially toward $2^N$ almost periodic encoded patterns. The obtained results are new, they extend and generalize the corresponding results existing in previous literature.Comment: 28 pages, 4 figure

Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument

We consider a new model for shunting inhibitory cellular neural networks, retarded functional differential equations with piecewise constant argument. The existence and exponential stability of almost periodic solutions are investigated. An illustrative example is provided.Comment: 24 pages, 1 figur

Mechanisms of Zero-Lag Synchronization in Cortical Motifs

Zero-lag synchronization between distant cortical areas has been observed in a diversity of experimental data sets and between many different regions of the brain. Several computational mechanisms have been proposed to account for such isochronous synchronization in the presence of long conduction delays: Of these, the phenomenon of "dynamical relaying" - a mechanism that relies on a specific network motif - has proven to be the most robust with respect to parameter mismatch and system noise. Surprisingly, despite a contrary belief in the community, the common driving motif is an unreliable means of establishing zero-lag synchrony. Although dynamical relaying has been validated in empirical and computational studies, the deeper dynamical mechanisms and comparison to dynamics on other motifs is lacking. By systematically comparing synchronization on a variety of small motifs, we establish that the presence of a single reciprocally connected pair - a "resonance pair" - plays a crucial role in disambiguating those motifs that foster zero-lag synchrony in the presence of conduction delays (such as dynamical relaying) from those that do not (such as the common driving triad). Remarkably, minor structural changes to the common driving motif that incorporate a reciprocal pair recover robust zero-lag synchrony. The findings are observed in computational models of spiking neurons, populations of spiking neurons and neural mass models, and arise whether the oscillatory systems are periodic, chaotic, noise-free or driven by stochastic inputs. The influence of the resonance pair is also robust to parameter mismatch and asymmetrical time delays amongst the elements of the motif. We call this manner of facilitating zero-lag synchrony resonance-induced synchronization, outline the conditions for its occurrence, and propose that it may be a general mechanism to promote zero-lag synchrony in the brain.Comment: 41 pages, 12 figures, and 11 supplementary figure

Exponential stability of delayed recurrent neural networks with Markovian jumping parameters

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.In this Letter, the global exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with time delays and Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the neural network is stochastically exponentially stable in the mean square, independent of the time delay. By employing a new Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions, and therefore the global exponential stability in the mean square for the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

A distributed networked approach for fault detection of large-scale systems

Networked systems present some key new challenges in the development of fault diagnosis architectures. This paper proposes a novel distributed networked fault detection methodology for large-scale interconnected systems. The proposed formulation incorporates a synchronization methodology with a filtering approach in order to reduce the effect of measurement noise and time delays on the fault detection performance. The proposed approach allows the monitoring of multi-rate systems, where asynchronous and delayed measurements are available. This is achieved through the development of a virtual sensor scheme with a model-based re-synchronization algorithm and a delay compensation strategy for distributed fault diagnostic units. The monitoring architecture exploits an adaptive approximator with learning capabilities for handling uncertainties in the interconnection dynamics. A consensus-based estimator with timevarying weights is introduced, for improving fault detectability in the case of variables shared among more than one subsystem. Furthermore, time-varying threshold functions are designed to prevent false-positive alarms. Analytical fault detectability sufficient conditions are derived and extensive simulation results are presented to illustrate the effectiveness of the distributed fault detection technique