Impulsive Cohen-Grossberg Research Articles

Stability for a retarded impulsive Cohen–Grossberg BAM neural network system

ABSTRACT In this paper, an impulsive Cohen-Grossberg bidirectional associative neural network with both time-varying and distributed delays is examined. Novel sufficient conditions for deriving stability with a desired rate, including the exponential one, are obtained. We consider a large class of admissible kernels encompassing the existing ones. Our findings cover the existing stability results in the literature. Finally, a numerical example is given for the validation of the theoretical outcomes.

Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.

Existence and stability of periodic solutions for impulsive fuzzy BAM Cohen-Grossberg neural networks on time scales

This paper is concerned with the existence and global exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg BAM neural networks on time scales. Applying the method of coincidence degree and constructing some suitable Lyapunov functional, we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg BAM neural networks on time scales. Moreover, we give an example to illustrate the results obtained.

Antiperiodic Solutions to Impulsive Cohen-Grossberg Neural Networks with Delays on Time Scales

We use the method of coincidence degree and construct suitable Lyapunov functional to investigate the existence and global exponential stability of antiperiodic solutions of impulsive Cohen-Grossberg neural networks with delays on time scales. Our results are new even if the time scaleT=RorZ. An example is given to illustrate our feasible results.

Improved Stability Estimates for Impulsive Delay Reaction-Diffusion Cohen-Grossberg Neural Networks Via Hardy-Poincaré Inequality

Abstract An impulsive Cohen-Grossberg neural network with time-varying and S-type distributed delays and reaction-diffusion terms is considered. By using Hardy-Poincaré inequality instead of Hardy-Sobolev inequality or just the nonpositivity of the reaction-diffusion operators, under suitable conditions in terms of M-matrices which involve the reaction-diffusion coefficients and the dimension and size of the spatial domain, improved stability estimates for the system with zero Dirichlet boundary conditions are obtained. Examples are given.

Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

This work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. By means of Poincaré inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The proposed criteria are relevant to the diffusion coefficients and the smallest positive eigenvalue of corresponding Dirichlet Laplacian. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.

Impulsive Cohen-Grossberg neural networks with s-type distributed delays

Abstract We study impulsive Cohen-Grossberg neural networks with S-type distributed delays. This type of delays in the presence of impulses is more general than the usual types of delays studied in the literature. Using analysis techniques we prove the existence of a unique equilibrium point. By means of simple and efficient Lyapunov functions we present some sufficient conditions for the exponential stability of the equilibrium.

Anti-periodic Solutions of Impulsive Cohen-Grossberg SICNNs on Time Scales

By using the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions areestablished for the existence and global exponential stability of anti-periodic solutions for a kind of impulsive Cohen-Grossberg shunting inhibitory cellular neural networks (CGSICNNs) on time scales. An example is given to illustrate ourresults.

Existence and Stability of Anti-periodic Solutions for an Impulsive Cohen-Grossberg SICNNs on Time Scales

Existence and Stability of Anti-periodic Solutions for an Impulsive Cohen-Grossberg SICNNs on Time Scales

STABILITY ANALYSIS OF IMPULSIVE COHEN-GROSSBERG NEURAL NETWORK WITH UNBOUNDED DISCRETE TIME-VARYING DELAYS

In this paper, the impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays is considered. By using the analysis method and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of the addressed neural network. These results generalize the existing relevant stability results. Two examples with simulations are given to show the effectiveness of the obtained results.