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A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays
This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this Letter, the analysis problem for the existence and stability of periodic solutions is investigated for a class of general discrete-time recurrent neural networks with time-varying delays. For the neural networks under study, a generalized activation function is considered, and the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. By employing the latest free-weighting matrix method, an appropriate LyapunovāKrasovskii functional is constructed and several sufficient conditions are established to ensure the existence, uniqueness, and globally exponential stability of the periodic solution for the addressed neural network. The conditions are dependent on both the lower bound and upper bound of the time-varying time delays. Furthermore, the conditions are expressed in terms of the linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Two simulation examples are given to show the effectiveness and less conservatism of the proposed criteria.This work was supported in part by the National Natural Science Foundation of China under Grant 50608072, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany
Multi-almost periodicity and invariant basins of general neural networks under almost periodic stimuli
In this paper, we investigate convergence dynamics of 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 almost periodic encoded patterns under
two classes of activation functions. By employing the property of
-cone and inequality technique, attracting basins are estimated
and some criteria are derived for the networks to converge exponentially toward
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
Convergence of asymptotic systems of non-autonomous neural network models with infinite distributed delays
In this paper we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.The paper was supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the "Fundacao para a Ciencia e a Tecnologia", through the Project PEstOE/MAT/UI0013/2014. The author thanks the referee for valuable comments.info:eu-repo/semantics/publishedVersio
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
On the validity of memristor modeling in the neural network literature
An analysis of the literature shows that there are two types of
non-memristive models that have been widely used in the modeling of so-called
"memristive" neural networks. Here, we demonstrate that such models have
nothing in common with the concept of memristive elements: they describe either
non-linear resistors or certain bi-state systems, which all are devices without
memory. Therefore, the results presented in a significant number of
publications are at least questionable, if not completely irrelevant to the
actual field of memristive neural networks
Analysis of global asymptotic stability and pseudo almost periodic solution of a class of chaotic neural networks
In this paper we give sufficient conditions ensuring the existence and uniqueness of pseudo almost periodic solution of a class of delayed chaotic neural networks. Further, we study the global asymptotic stability (GAS) of the considered model and give a set of criteria on (GAS) by constructing new Lyapunov functional
Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions
In this manuscript we analyze the collective behavior of mean-field limits of
large-scale, spatially extended stochastic neuronal networks with delays.
Rigorously, the asymptotic regime of such systems is characterized by a very
intricate stochastic delayed integro-differential McKean-Vlasov equation that
remain impenetrable, leaving the stochastic collective dynamics of such
networks poorly understood. In order to study these macroscopic dynamics, we
analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics
and sigmoidal interactions. In that case, we prove that the solution of the
mean-field equation is Gaussian, hence characterized by its two first moments,
and that these two quantities satisfy a set of coupled delayed
integro-differential equations. These equations are similar to usual neural
field equations, and incorporate noise levels as a parameter, allowing analysis
of noise-induced transitions. We identify through bifurcation analysis several
qualitative transitions due to noise in the mean-field limit. In particular,
stabilization of spatially homogeneous solutions, synchronized oscillations,
bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from
static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow
further exploring the role of noise in the nervous system.Comment: Updated to the latest version published, and clarified the dependence
in space of Brownian motion
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