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On the exponential stability of a neutral differential equation of first order

Gözen M., Tunç C.

Journal of Mathematics and Applications

2018

Vol. 41

95--107

In this work, we establish some assumptions that guaranteeing the global exponential stability (GES) of the zero solution of a neutral differential equation (NDE). We aim to extend and improves some results found in the literature.

Stability of nonlinear Volterra equations

Ngoc P. H. A., Hieu L. T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 3

333--340

Using a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform attraction of equilibrium of discrete-time bidirectional associative memory (BAM) neural networks. Some illustrative examples are given.

On Exponential Stability of Volterra Difference Equations with Infinite Delay

Ngoc P. H. A., Hieu L. T.

Bulletin of the Polish Academy of Sciences. Mathematics

2014

Vol. 62, no 2

125--137

General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Zhang Q., Yang L., Liao D.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 4

649-658

Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.