In this paper, a definition of the fundamental operator for the linear autonomous functional differential equation with infinite delay in a Banach space is given, and some sufficient and necessary conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponentia...

This paper is concerned with the existence and exponential stability of anti-periodic solutions of a class of shunting inhibitory cellular neural networks with continuously distributed delays and time-varying delays in the leakage terms. By using differential inequality techniques, some verifiable and practical delay-dependent criteria on the existence and exponential stability of anti-periodic...

This brief presents new theoretical results on the global exponential stability of neural networks with time-varying delays and Lipschitz continuous activation functions. These results include several sufficient conditions for the global exponential stability of general neural networks with time-varying delays and without monotone, bounded, or continuously differentiable activation function. In...

to be exponentially stable and to apply these results to the study of change of stability in parameter dependent time-periodic parabolic problems. Here, !:::.. denotes the Laplacian in JRN and the weight-function lies in C~(JR, BUC(JRN)), the space of v-HOlder continuous and T -periodic functions taking values in the space of bounded uniformly continuous functions on JRN (v E (0, 1) and T > 0 f...

This paper deals with the problem of exponential stability of linear switched delay systems. An average dwell time method is introduced into linear switched delay systems for the first time and LMIs’ conditions are presented to guarantee robust exponential stability of such systems. A lower bound of average dwell time is given. Exponential decay estimates for the states of such systems are also...

This paper studies the pth moment exponential synchronization of a class of stochastic neural networks with mixed delays. Based on Lyapunov stability theory, by establishing a new integrodifferential inequality with mixed delays, several sufficient conditions have been derived to ensure the pth moment exponential stability for the error system. The criteria extend and improve some earlier resul...

Making use of the generalized time scales exponential function, we give a new definition for the exponential stability of solutions for dynamic equations on time scales. Employing Lyapunov-type functions on time scales, we investigate the boundedness and the exponential stability of solutions to first-order dynamic equations on time scales, and some sufficient conditions are obtained. Some exam...

We study the existence and global exponential stability of positive periodic solutions for a class of continuous-time generalized bidirectional neural networks with variable coefficients and delays. Discrete-time analogues of the continuous-time networks are formulated and the existence and global exponential stability of positive periodic solutions are studied using the continuation theorem of...

In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of perio...

The exponential stability of continuous-time Hopfield neural networks is not preserved when implemented on digital computers by means of explicit numerical methods, whereas the implicit (or backward) Euler method preserves this exponential stability under exactly the same sufficient conditions as those previously obtained for the continuous model. The proof is based on the nonlinear measure app...