Discrete-time Cohen Grossberg Neural Networks Research Articles

Almost automorphic behaviours of nonlocal stochastic fuzzy Cohen–Grossberg lattice neural networks

Discrete-time Cohen–Grossberg neural networks (CGNNs) play important role in feedback neural networks. The existing literatures of CGNNs only regarded integral order discrete-time models without other variables. This paper builds the lattice model for nonlocal stochastic fuzzy CGNNs with reaction diffusions by employing the finite difference and Mittag–Leffler time Euler difference techniques. Further, the existence of a unique bounded almost automorphic sequence solution in distribution and global exponential convergence in the mean-square sense to the achieved difference model are investigated. At last, by using the tool of Matlab and time Euler difference for the Brownian motions, an illustrative example with simulations is used to show the feasible of the works of the current paper. We think that this work can contribute to achieve some effective real tasks, e.g. content-addressable memory, auto-association, dynamic reconstruction of a chaotic process, etc.

Exponential stability and synchronisation of fuzzy Mittag–Leffler discrete-time Cohen–Grossberg neural networks with time delays

Exponential Euler differences for semi-linear differential equations of first order have got rapid development in the past few years and a variety of exponential Euler difference methods have become very significant researching topics. Therefore, exponential Euler differences for fractional-order differential models are novel and significant. In allusion to fuzzy Cohen–Grossberg neural networks of fractional order, this paper establishes a Mittag–Leffler Euler difference model on the basis of the constant variation formula in fractional calculus. In the second place, the existence of a unique global bounded solution and equilibrium point is studied by using the contractive mapping principle. Thirdly, global exponential stability and synchronisation of the derived difference models are investigated by employing some inequality techniques and reductio. At last, some illustrative examples and numerical simulations are employed to demonstrate the main results of this paper.

Global asymptotic stability for discrete-time Cohen-Grossberg neural networks with delays by combining graph theoretic approach with Homeomorphism concept

ABSTRACT In this paper, global asymptotic stability for a class of discrete-time Cohen-Grossberg Neural Networks with finite and infinite delays is investigated. By combining graph theoretic approach with Homeomorphism concept as well as Lyapunov functional method, two new sufficient conditions ensuring the global asymptotic stability of equilibrium point for above neural networks are established. Combining graph theoretic approach with Homeomorphism concept studies the equilibrium point of neural networks is a novel approach.

A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks

Abstract This paper focuses on the problem of global exponential stability analysis for high-order delayed discrete-time Cohen–Grossberg neural networks. Multiple time-varying delays are considered. First, a technique lemma is obtained based on the properties of nonsingular M-matrices. Second, the delay-dependent and -independent criteria under which the zero equilibrium is globally exponentially stable are derived, respectively. Last, the validity of these criteria are illustrated by a pair of numerical examples. Compared with the previous results, the merits of the proposed method are: (i) no Lyapunov–Krasovskii functional or auxiliary function is required; (ii) less computational complexity is verified; and (iii) the obtained stability criteria can easily be realized, since they are to test whether a matrix is nonsingular M-matrix.

Lagrange Stability for Delayed-Impulses in Discrete-Time Cohen–Grossberg Neural Networks with Delays

In this paper, the problem of exponential Lagrange stability for delayed-impulses in discrete-time Cohen–Grossberg neural networks (CGNNs) with delays is considered. By establishing a novel convergent difference inequation, combining with inductive method and Lyapunov theory, some sufficient conditions are obtained to ensure the exponential Lagrange stability for delayed-impulses in discrete-time CGNNs. Meanwhile, the exponential convergent domain for network is given. Finally, some examples with their simulations are given to verify the effectiveness of our results.

Periodic solutions for discrete-time Cohen–Grossberg neural networks with delays

In this paper, the existence of periodic solutions for general discrete-time Cohen–Grossberg neural networks with delays (DCGNND) is investigated. Based on graph theory, coincidence degree theory, and Lyapunov method, a sufficient criterion ensuring the existence of periodic solutions for DCGNND is established. In the end, an example and its numerical simulation are given to demonstrate the effectiveness of the theoretical result.

Periodic solutions of discrete time periodic time-varying coupled systems on networks

In this paper, we consider the existence of periodic solutions for discrete time periodic time-varying coupled systems on networks (DPTCSN). Some novel sufficient conditions are obtained to guarantee the existence of periodic solutions for DPTCSN, which have a close relation to the topology property of the corresponding network. Our approach is based on the continuation theorem of coincidence degree theory, generalized Kirchhoff’s matrix tree theorem in graph theory, Lyapunov method and some new analysis techniques. The approach is applied to the existence of periodic solutions for discrete time Cohen–Grossberg Neural Networks (CGNN). Finally, an example and numerical simulations are provided to illustrate the effectiveness of our theoretical results.

Dynamic analysis of periodic solution for high-order discrete-time Cohen–Grossberg neural networks with time delays

In this paper, we analyze the dynamic behavior of periodic solution for the high-order discrete-time Cohen–Grossberg neural networks (CGNNs) with time delays. First, the existence is studied based on the continuation theorem of coincidence degree theory and Young’s inequality. And then, the criterion for the global exponential stability is given using Lyapunov method. Finally, simulation result shows the effectiveness of our proposed criterion.

Existence and stability of periodic solution of high-order discrete-time Cohen–Grossberg neural networks with varying delays

Abstract This paper studies the existence and stability of periodic solution of the high-order discrete-time Cohen–Grossberg neural networks with varying delays. The properties of M-matrix and the contracting mapping principle are used to obtain a sufficient condition that guarantees the uniqueness and global exponential stability of the periodic solution. In addition, a numerical example is given that demonstrates the effectiveness of the proposed theoretical results.

Existence and stability of periodic solutions of discrete-time Cohen–Grossberg neural networks with delays and impulses

In this paper, a class of discrete-time Cohen–Grossberg neural networks with delays and impulses is investigated. First, the existence of periodic solution for the addressed neural networks is proposed by applying Mawhin׳s continuation theorem. Besides, some sufficient conditions are given to guarantee global stability of periodic solution by using Lyapunov functional method and some analysis techniques. Finally, an example with numerical simulation is given to demonstrate the effectiveness of the obtained results.

Stability and Bifurcation of a Class of Discrete-Time Cohen–Grossberg Neural Networks with Discrete Delays

A class of discrete-time Cohen---Grossberg neural networks with discrete delays and ring-architecture are investigated in this paper. By analyzing the corresponding characteristic equations, the existence of Neimark---Sacker bifurcations at the origin are obtained. By applying the normal form theory and the center manifold theorem, the direction of the Neimark---Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Sufficient conditions to guarantee the global stability of the null solution of such networks are established by using suitable Lyapunov function and the properties of M-matrix. Numerical simulations are given to illustrate the obtained results.

Global Attractivity of Almost Periodic Sequence Solutions of Delayed Discrete-Time Neural Networks

This paper examines the existence and global attractivity of a unique almost periodic sequence solution for a class of discrete-time Cohen–Grossberg neural networks with delays, for which some sufficient conditions are obtained. Moreover, a computer simulation is given to illustrate the correctness of our results.

Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays

A class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations are discussed. By applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the obtained results.

Global stability of discrete-time Cohen–Grossberg neural networks with impulses

Discrete-time impulsive Cohen–Grossberg neural network (CGNN) with and without delayed time is studied in this paper. Some stability criteria are obtained to ensure the global asymptotic/exponential stability of the equilibrium point of discrete-time impulsive CGNN by discrete-time Halanay inequality. It is shown that the discrete-time impulsive CGNN can achieve the global exponential stability of the impulse-free CGNN even if the impulses have enlarging effects on the states of neurons.

Synchronization control for arrays of coupled discrete-time delayed Cohen–Grossberg neural networks

This paper investigates the global exponential synchronization for an array of coupled discrete-time Cohen–Grossberg neural networks (CGNNs) with time-varying delay, in which both the constant coupling and delayed one are considered. Through constructing an improved Lyapunov–Krasovskii functional, the delay-dependent sufficient condition is obtained to guarantee the global synchronization based on linear matrix inequality (LMI) approach. The criterion is presented in terms of LMIs and its feasibility can be easily checked by resorting to Matlab LMI Toolbox. Moreover, the addressed system can include some famous neural network models as its special cases, which can help extend those present results. Finally, the effectiveness of the proposed method can be further illustrated with the help of two numerical examples.

Discrete-time Cohen-Grossberg neural networks with transmission delays and impulses

Abstract A discrete-time analogue is formulated for an impulsive Cohen- -Grossberg neural network with transmission delay in a manner in which the global exponential stability characterisitics of a unique equilibrium point of the network are preserved. The formulation is based on extending the existing semidiscretization method that has been implemented for computer simulations of neural networks with linear stabilizing feedback terms. The exponential convergence in the p-norm of the analogue towards the unique equilibrium point is analysed by exploiting an appropriate Lyapunov sequence and properties of an M-matrix. The main result yields a Lyapunov exponent that involves the magnitude and frequency of the impulses. One can use the result for deriving the exponential stability of non-impulsive discrete-time neural networks, and also for simulating the exponential stability of impulsive and non-impulsive continuous-time networks.

Global asymptotic stability analysis of discrete-time Cohen–Grossberg neural networks based on interval systems

The global asymptotic stability of discrete-time Cohen–Grossberg neural networks (CGNNs) with or without time delays is studied in this paper. The CGNNs are transformed into discrete-time interval systems, and several sufficient conditions for asymptotic stability for these interval systems are derived by constructing some suitable Lyapunov functionals. The conditions obtained are given in the form of linear matrix inequalities that can be checked numerically and very efficiently by using the MATLAB LMI Control Toolbox. Finally, some illustrative numerical examples are provided to demonstrate the effectiveness of the results obtained.

Global exponential stability of discrete-time Cohen–Grossberg neural networks

Discrete-time versions of the continuous-time Cohen–Grossberg neural networks (CGNNs) are formulated and studied in this paper. Several sufficient conditions are obtained to ensure the global exponential stability of the discrete-time systems of CGNNs with and without delays based on Lyapunov methods. The obtained results have not assume the symmetry of the connection matrix, and monotonicity and the differentiability of the activation functions.