Class Of Cohen-Grossberg Neural Networks Research Articles

Finite-/fixed-time synchronization for Cohen-Grossberg neural networks with discontinuous or continuous activations via periodically switching control.

This paper is concerned with finite-/fixed-time synchronization for a class of Cohen-Grossberg neural networks with discontinuous or continuous activations and mixed time delays. Based on the finite-time stability theory, Lyapunov stability theory, the concept of Filippov solution and the differential inclusion theory, some useful finite-/fixed-time synchronization sufficient conditions for the considered Cohen-Grossberg neural networks are established by designing two kinds of novel periodically switching controllers. Instead of using uninterrupted high control strength, the periodically switching controller in each period is used with high strength control in one stage and weak strength in the other. It can overcome the effects caused by the uncertainties of Filippov solution induced by discontinuous neuron activation functions and reduce the control cost. Besides, the period switching control rate is closely related to the settling time T. Finally, two numerical examples are given to demonstrate the effectiveness and feasibility of the obtained results.

Further stability analysis of neutral-type Cohen-Grossberg neural networks with multiple delays

The key contribution of this paper is to study the stability analysis of neutral-type Cohen-Grossberg neural networks possessing multiple time delays in the states of the neurons and multiple neutral delays in time derivative of states of the neurons. By making the use of a proper Lyapunov functional, we propose a novel sufficient time-independent stability criterion for this model of neutral-type neural networks. The proposed stability criterion in this paper can be absolutely expressed in terms of the parameters of the neural network model considered as this newly proposed criterion only relies on the relationships established among the network parameters. A numerical example is also given to indicate the advantages of the obtained stability criterion over the previously published stability results for the same class of Cohen-Grossberg neural networks. Since obtaining stability conditions for neutral-type Cohen-Grossberg neural networks with multiple delays is a difficult task to achieve, there are only few papers in the literature dealing with this problem. Therefore, the results given in the current paper makes an important contribution to the stability problem for this class of neutral-type neural networks.

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

Existence and exponential stability of pseudo almost automorphic solutions for Cohen-Grossberg neural networks with mixed delays

In this paper, we consider a class of Cohen-Grossberg neural networks with mixed delays. Different from the previous literature, we study the existence and exponential stability of pseudo almost automorphic solutions for the suggested system. Our method is mainly based on the Banach fixed point theorem and the Lyapunov functional method. Moreover, a numerical example is given to show the effectiveness of the main results.

Exponential Stability of Cohen-Grossberg Neural Networks with Impulse Time Window

This paper concerns the problem of exponential stability for a class of Cohen-Grossberg neural networks with impulse time window and time-varying delays. In our letter, the impulsive effects we considered can stochastically occur at a definitive time window and the impulsive controllers we considered can be nonlinear and even rely on the states of all the neurons. Hence, the impulses here can be more applicable and more general. By utilizing Lyapunov functional theory, inequality technique, and the analysis method, we obtain some novel and effective exponential stability criteria for the Cohen-Grossberg neural networks. These results generalize a few previous known results and numerical simulations are given to show the effectiveness of the derived results.

New delay-dependent stability criteria for cohen-grossberg neural networks with multiple time-varying mixed delays

This paper investigates the globally asymptotical stability problem for a general class of Cohen-Grossberg neural networks with multiple mixed time-delays. Before proving the main theorem, a more generalized convex combination inequality is proposed. A new stability criterion for Cohen-Grossberg neural networks with multiple time-varying delays is obtained by the employed general inequality technique. Two examples are included to illustrate the effectiveness of the presented results.

Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure thatn-dimensional Cohen-Grossberg neural networks withk-level discontinuous activation functions can haveknequilibrium points orknperiodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results.

Adaptive lag synchronization of chaotic Cohen-Grossberg neural networks with discrete delays

A class of Cohen-Grossberg neural networks with discrete delays are investigated in this paper. By using the suitable Lyapunov function, sufficient conditions for adaptive lag synchronization of such systems are obtained. Finally, a numerical example is given to demonstrate the main results.

Global Exponential Stability Analysis for Cohen-Grossberg Neural Networks with Non-Lipschitz Neuron Activations

In this paper，a novel class of Cohen-Grossberg neural networks with inverse Hlder neuron activation functions is presented. By employing the Brouwer degree properties and linear matrix inequality techniques, the existence and uniqueness of equilibrium point for such Cohen-Grossberg neural networks are investigated. By constructing appropriate Lyapunov functions and using Lyapunov diagonally stable matrices, a sufficient condition which is used to checked the global exponential stability of a unique equilibrium point is established. A numerical example is given to demonstrate the effectiveness of the theoretical results.

Asymptotical Mean Square Stability of Cohen-Grossberg Neural Networks with Random Delay

The asymptotical mean-square stability analysis problem is considered for a class of Cohen-Grossberg neural networks (CGNNs) with random delay. The evolution of the delay is modeled by a continuous-time homogeneous Markov process with a finite number of states. The main purpose of this paper is to establish easily verifiable conditions under which the random delayed Cohen-Grossberg neural network is asymptotical mean-square stability. By employing Lyapunov-Krasovskii functionals and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria for the asymptotical mean-square stability, which can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.

Global Asymptotic Stability and Robust Stability of a Class of Cohen–Grossberg Neural Networks With Mixed Delays

This paper is concerned with the global asymptotic stability of a class of Cohen-Grossberg neural networks with both multiple time-varying delays and continuously distributed delays. Two classes of amplification functions are considered, and some sufficient stability criteria are established to ensure the global asymptotic stability of the concerned neural networks, which can be expressed in the form of linear matrix inequality and are easy to check. Furthermore, some sufficient conditions guaranteeing the global robust stability are also established in the case of parameter uncertainties.

Robust Stability of Cohen–Grossberg Neural Networks via State Transmission Matrix

This brief is concerned with the global robust exponential stability of a class of interval Cohen-Grossberg neural networks with both multiple time-varying delays and continuously distributed delays. Some new sufficient robust stability conditions are established in the form of state transmission matrix, which are different from the existing ones. Furthermore, a sufficient condition is also established to guarantee the global stability for this class of Cohen-Grossberg neural networks without uncertainties. Three examples are used to show the effectiveness of the obtained results.

Global stability of a class of Cohen-Grossberg neural networks with delays

This paper is concerned with the Global Asymptotic Stability (GAS) of a general class of Cohen-Grossberg neural networks with both multiple time varying delays and distributed delays. Criteria are established to ensure the GAS of the concerned neural networks, which can be expressed in the form of Linear Matrix Inequality and independent of amplification functions. Furthermore, a sufficient condition guaranteeing the global robust stability is established for the general class of Cohen-Grossberg neural networks with both multiple time varying delays and distributed delays in the case of parameter uncertainties.

Global stability of Cohen-Grossberg neural networks with time-varying and distributed delays

In this paper, the global asymptotic stability is investigated for a class of Cohen-Grossberg neural networks with time-varying and distributed delays. By using the Lyapunov-Krasovskii functional and equivalent descriptor form of the considered system, several delay-dependent sufficient conditions are obtained to guarantee the asymptotic stability of the addressed systems. These conditions are dependent on both time-varying and distributed delays and presented in terms of LMIs and therefore, the stability criteria of such systems can be checked readily by resorting to the Matlab LMI toolbox. Finally, an example is given to show the effectiveness and less conservatism of the proposed methods.