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In this paper, we present a method to achieve exponential stability in a class of impulsive delayed neural networks containing parameter uncertainties, time-varying delays, and impulsive effect and reaction–diffusion terms. By using an integro-differential inequality with impulsive initial conditions and employing the M-matrix theory and the nonlinear measure approach, some new sufficient conditions ensuring the global exponential stability and global robust exponential stability of the considered system are derived. In particular, the results obtained are presented by simple algebraic inequalities, which are certainly more concise than the previous methods. By comparisons and examples, it is shown that the results obtained are effective and useful. [ABSTRACT FROM AUTHOR]

In this paper, the periodicity of a class of nonautonomous fuzzy neural networks with impulses, reaction-diffusion terms, and distributed time delays are investigated. By establishing an integro-differential inequality with impulsive initial conditions and time-varying coefficients, employing the M -matrix theory, Poincar mappings, and fixed point theory, several new sufficient conditions to ensure the periodicity and global exponential stability of the formulated system are obtained. It is worthwhile to mention that our technical methods are practical, in the sense that all new stability conditions are stated in simple algebraic forms, and an optimization method is provided to estimate the exponential convergence rate, so their verification and applications are straightforward and convenient. The validity and generality of our methods are illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global exponential stability and periodicity of nonautonomous cellular neural networks with reaction-diffusion, impulses, and time-varying delays. By establishing a new differential inequality for nonautonomous systems, using the properties of M-matrix and inequality techniques, some new sufficient conditions for the global exponential stability of the system are obtained. Moreover, sufficient conditions for the periodic solutions of the system are obtained by using the Poincare mapping and the fixed point theory. The validity and superiority of the main results are verified by numerical examples and simulations. [ABSTRACT FROM AUTHOR]