Cohen-Grossberg Neural Networks Research Articles

Asymptotical and adaptive synchronization of Cohen–Grossberg neural networks with heterogeneous proportional delays

Abstract In this paper, the synchronization of Cohen–Grossberg neural networks with proportional delays is investigated. Firstly, the asymptotical synchronization is proposed by designing a simple linear feedback controller, and some delay-independent and delay-dependent criteria are derived based on variable transformation, reduction to absurdity and Lyapunov functional theory. In addition, an adaptive control strategy is designed to reduce the control cost and the adaptive synchronization is investigated by means of Barbalat lemma. Finally, two numerical examples are given to show the validity and effectiveness of the theoretical results.

Mittag-Leffler stability analysis of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument

This paper is concerned with the Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. Applying the Lyapunov method, the generalized Gronwall-Bellman inequality, and the theory of fractional-order differential equations, sufficient conditions are presented to guarantee the existence and uniqueness of solution. Besides, the global Mittag-Leffler stability is investigated. The obtained criteria are useful in the analysis and design of fractional-order fuzzy Cohen-Grossberg neural networks with deviating argument. A numerical example is given to substantiate the validity of the theoretical results.

Passivity and synchronization of coupled reaction–diffusion Cohen–Grossberg neural networks with state coupling and spatial diffusion coupling

This paper deals with the passivity and synchronization problems for two types of coupled reaction–diffusion Cohen–Grossberg neural networks (CRDCGNNs). On the one side, a CRDCGNNs model with state coupling is introduced, and several sufficient conditions which ensure the passivity and synchronization of this type of network are deduced respectively by resorting to some inequality techniques and Lyapunov functional method. On the other side, considering that the different diffusion of each node may give rise to different changes of other nodes in reaction–diffusion networks, we also carry out some investigations on the passivity and synchronization of CRDCGNNs with spatial diffusion coupling. Finally, the correctness of the obtained research results are corroborated by two illustrative examples.

Finite time synchronization of memristor-based Cohen-Grossberg neural networks with mixed delays.

Finite time synchronization, which means synchronization can be achieved in a settling time, is desirable in some practical applications. However, most of the published results on finite time synchronization don’t include delays or only include discrete delays. In view of the fact that distributed delays inevitably exist in neural networks, this paper aims to investigate the finite time synchronization of memristor-based Cohen-Grossberg neural networks (MCGNNs) with both discrete delay and distributed delay (mixed delays). By means of a simple feedback controller and novel finite time synchronization analysis methods, several new criteria are derived to ensure the finite time synchronization of MCGNNs with mixed delays. The obtained criteria are very concise and easy to verify. Numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

General decay synchronization of memristor-based Cohen–Grossberg neural networks with mixed time-delays and discontinuous activations

This paper investigates the general decay synchronization (GDS) of memristor-based Cohen–Grossberg neural networks (MCGNNs) with discontinuous neuron activation functions and mixed time-delays. Based on the concept of Filippov solution and theory of differential inclusion, introducing suitable Lyapunov–Krasovskii functionals and employing useful inequality techniques, some novel criteria ensuring the GDS of considered Cohen–Grossberg neural networks are established via two types of nonlinear controls. In addition, the feasibility of the obtained theoretical results is validated via two numerical examples and their simulations. The polynomial synchronization, asymptotical synchronization, and exponential synchronization can be seen the special cases of the GDS. To the authors’ knowledge, the results established in the paper are the only available results on the synchronization of neural networks, connecting the three main characteristics, i.e., memristor, discontinuous activation functions and mixed time-delays.

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.

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.

Exponential and fixed-time synchronization of Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms

This paper is devoted to the global exponential and fixed-time synchronization of delayed reaction-diffusion Cohen–Grossberg neural networks. Adaptive controllers are designed such that the addressed system can realize global exponential synchronization goal under the framework of inequality techniques, Lyapunov method as well as some suitable assumptions. Furthermore, as corollaries, the corresponding conclusion is provided to ensure the delayed Cohen–Grossberg neural networks without reaction-diffusion term can reach fixed-time synchronization goal. In addition, the settling time of fixed-time synchronization can be adjusted to desired values regardless of initial conditions, which is more reasonable. Finally, two numerical examples and its simulations are given to show the effectiveness of the obtained results.

Synchronization analysis for stochastic reaction-diffusion Cohen-Grossberg neural networks with Neumann boundary conditions via periodically intermittent control

In this paper, mathematical analysis is proposed on the synchronization problem for stochastic reaction-diffusion Cohen-Grossberg neural networks with Neumann boundary conditions. By introducing several important inequalities and using Lyapunov functional technique, some new synchronization criteria in terms of p-norm are derived under periodically intermittent control. Some previous known results in the literature are improved, and some restrictions on the mixed time-varying delays are removed. The influence of diffusion coefficients, diffusion space, stochastic perturbation and control width on synchronization is analyzed by the obtained synchronization criteria. Numerical simulations are presented to show the feasibility of the theoretical results.

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks driven by G-Brownian motion

ABSTRACTThis paper is devoted to study the stability of a class of impulsive stochastic Cohen–Grossberg neural networks driven by G-Brownian motion. By means of G-Lyapunov function, Borel–Cantelli lemma and inequality technique, a series of sufficient conditions on pth moment stability and quasi-sure stability with respect to a general decay function are established. A concrete example is given to illustrate the obtained results.

Stability switches in a Cohen–Grossberg neural network with multi-delays

In this paper, we consider a Cohen–Grossberg neural network with three delays. Regarding time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for time delays under certain conditions and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are given to illustrate the obtained results and interesting network behaviors are observed, such as multiple stability switches of the network equilibrium and synchronous (asynchronous) oscillations.

Anti-periodic solutions for BAM-type Cohen-Grossberg neural networks with time delays

Anti-periodic solutions for BAM-type Cohen-Grossberg neural networks with time delays

Finite-time synchronization by switching state-feedback control for discontinuous Cohen–Grossberg neural networks with mixed delays

This paper studies the finite-time synchronization problem of Cohen–Grossberg neural networks (CGNNs) with discontinuous neuron activations and mixed time-delays. Under the extended differential inclusion framework, the famous finite-time stability theorem and generalized Lyapunov approach are used to realize the finite-time synchronization control of drive-response system. Different from the conventional controllers, we propose two classes of novel switching state-feedback controllers which include discontinuous factor sign ( $$\cdot$$ ). By doing so, the synchronization error of CGNNs can be controlled to converge zero in a finite time. Moreover, we also provide an estimation of the upper bound of the settling time for synchronization. Finally, two examples and simulation experiment are given to demonstrate the validity of theoretical results.

Exponential Stability of Periodic Solution for Impulsive Memristor-Based Cohen–Grossberg Neural Networks with Mixed Delays

Memristor, as the future of artificial intelligence, has been widely used in pattern recognition or signal processing from sensor arrays. Memristor-based recurrent neural network (MRNN) is an ideal model to mimic the functionalities of the human brain due to the physical properties of memristor. In this paper, the periodicity for memristor-based Cohen–Grossberg neural networks (MCGNNs) is studied. The neural network (NN) considered in this paper is based on the memristor and involves time-varying delays, distributed delays and impulsive effects. The boundedness and monotonicity of the activation function are not assumed. By some inequality technique and contraction mapping principle, we prove the existence, uniqueness and exponential stability of periodic solution for MCGNNs. Finally, some numeral examples and comparisons are provided to illustrate the validation of our results.

Passivity analysis of delayed reaction-diffusion Cohen-Grossberg neural networks via Hardy-Poincarè inequality

In this paper, we formulate and investigate the passivity analysis of delayed reaction-diffusion neural networks with Cohen-Grossberg type. The derivative of the Lyapunov-Krasovskii functional was estimated by the new agencies of Hardy-Poincarè inequality and some analysis techniques. Subsequently, some new and concise conditions to check the passivity of the given Cohen-Grossberg neural networks were summarized. The proposed criteria not only depends on the system parameters, reaction-diffusion coefficients but also on the regional feature. Furthermore, as corollaries, some sufficient schemes are provided to achieve passive and exponential passive of delayed Cohen-Grossberg neural networks without reaction-diffusion term. The results obtained in this paper generalize and improve many known results. Finally, two numerical examples and its simulations are proposed to show the effectiveness and merits of the improved theoretical results.

Exponential stability criteria for fuzzy bidirectional associative memory Cohen-Grossberg neural networks with mixed delays and impulses

This paper is concerned with fuzzy bidirectional associative memory (BAM) Cohen-Grossberg neural networks with mixed delays and impulses. By constructing an appropriate Lyapunov function and a new differential inequality, we obtain some sufficient conditions which ensure the existence and global exponential stability of a periodic solution of the model. The results in this paper extend and complement the previous publications. An example is given to illustrate the effectiveness of our obtained results.

Existence, uniqueness and stability of mild solutions to stochastic reaction–diffusion Cohen–Grossberg neural networks with delays and Wiener processes

In this paper, we study delayed reaction–diffusion Cohen–Grossberg neural networks driven by infinite dimensional Wiener processes. Based on semigroup theory, existence and uniqueness of mild solutions are proved under global Lipschitz conditions. Then, some criteria of global exponential stability are obtained by using Lyapunov method and Halanay inequality. Finally, some interesting examples are provided to show the feasibility and usefulness of the developed results.

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.

Exponential synchronization of Cohen-Grossberg neural networks with stochastic perturbation and reaction-diffusion terms via periodically intermittent control

In this paper, a class of Cohen-Grossberg neural networks with mixed time-varying delays, stochastic perturbation and reaction-diffusion terms is investigated. The exponential synchronization criteria in terms of p-norm are obtained based on periodically intermittent control by means of Lyapunov functional theory, mathematical induction and inequality technique. The influences of stochastic perturbation, spacial diffusion, the control rate and the control strength on the exponential synchronization are discussed according to the obtained synchronization criteria. The proposed criteria improve the previous known results in the literature and remove the restrictions on the mixed time-varying delays. Numerical simulations are carried out to illustrate the feasibility of the results. https://doi.org/10.28919/cmbn/2853

Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.