pth moment exponential stability of stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays

In this paper, stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are investigated. By using Lyapunov function and the Ito differential formula, some sufficient conditions for the pth moment exponential stability of such stochastic fuzzy Cohen–Grossberg neural networks with discrete and distributed delays are established. An example is given to illustrate the feasibility of our main theoretical findings. Finally, the paper ends with a brief conclusion. Methodology and achieved results is to be presented

Anti-periodic solution for fuzzy Cohen–Grossberg neural networks with time-varying and distributed delays

In this paper, by using a continuation theorem of coincidence degree theory and a differential inequality, we establish some sufficient conditions ensuring the existence and global exponential stability of anti-periodic solutions for a class of fuzzy Cohen–Grossberg neural networks with time-varying and distributed delays. In addition, we present an illustrative example to show the feasibility of obtained results

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

Global asymptotic stability of nonautonomous Cohen-Grossberg neural network models with infinite delays

For a general Cohen-Grossberg neural network model with potentially unbounded time-varying coeffi cients and infi nite distributed delays, we give su fficient conditions for its global asymptotic stability. The model studied is general enough to include, as subclass, the most of famous neural network models such as Cohen-Grossberg, Hopfi eld, and bidirectional associative memory. Contrary to usual in the literature, in the proofs we do not use Lyapunov functionals. As illustrated, the results are applied to several concrete models studied in the literature and a comparison of results shows that our results give new global stability criteria for several neural network models and improve some earlier publications.The second author research was suported 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 authors thank the referee for valuable comments

New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays

A new global asymptotic stability criterion of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with probabilistic time-varying delays was derived, in which the diffusion item can play its role. Owing to deleting the boundedness conditions on amplification functions, the main result is a novelty to some extent. Besides, there is another novelty in methods, for Lyapunov-Krasovskii functional is the positive definite form of p powers, which is different from those of existing literature. Moreover, a numerical example illustrates the effectiveness of the proposed methods

Finite-time stabilization of discontinuous fuzzy inertial Cohen–Grossberg neural networks with mixed time-varying delays

This article aims to study a class of discontinuous fuzzy inertial Cohen–Grossberg neural networks (DFICGNNs) with discrete and distributed time-delays. First of all, in order to deal with the discontinuities by the differential inclusion theory, based on a generalized variable transformation including two tunable variables, the mixed time-varying delayed DFICGNN is transformed into a first-order differential system. Then, by constructing a modified Lyapunov–Krasovskii functional concerning with the mixed time-varying delays and designing a delayed feedback control law, delay-dependent criteria formulated by algebraic inequalities are derived for guaranteeing the finite-time stabilization (FTS) for the addressed system. Moreover, the settling time is estimated. Some related stability results on inertial neural networks is extended. Finally, two numerical examples are carried out to verify the effectiveness of the established results

LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω), Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays

Generalized non-autonomous Cohen-Grossberg neural network model

In the present paper, we investigate both the global exponential stability and the existence of a periodic solution of a general differential equation with unbounded distributed delays. The main stability criterion depends on the dominance of the non-delay terms over the delay terms. The criterion for the existence of a periodic solution is obtained with the application of the coincide degree theorem. We use the main results to get criteria for the existence and global exponential stability of periodic solutions of a generalized higher-order periodic Cohen-Grossberg neural network model with discrete-time varying delays and infinite distributed delays. Additionally, we provide a comparison with the results in the literature and a numerical simulation to illustrate the effectiveness of some of our results.Comment: 30 page

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

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