On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

Abstract

The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural network model under consideration. By means of the Lyapunov function method sufficient conditions that guarantee the stability properties of solutions are established. Two examples are presented to show the validity of the proposed stability criteria.

Information Processing with Stability Point Modeling in Cohen–Grossberg Neural Networks

“…The major findings concerning the equilibrium state of the (20) model's h stability are taken into consideration. The authored lemma and authored theorem are found in [16][17][18]. Equation ( 20) was taken from [17], which presents the theoretical model mentioned in Theorem 1 from the same paper.…”

“…( 1 w 2 ) T a 1 = 0.9 0.45 0.2 0.8 = 0.54 (16) ( 2 w 2 ) T a 1 = 0.45 0.9 0.2 0.8 = 0.81 (17) As a result, the input to the second neuron is 1.5 times that of the first neuron. However, after a quarter of a second, the second neuron's output surpasses that of the first neuron by a factor of 6.34.…”

Impulsive Control Via Variable Impulsive Perturbations on a Generalized Robust Stability for Cohen–Grossberg Neural Networks With Mixed Delays

“…However, due to the complexity of the problem, the reported results on h−manifolds stability for Cohen-Grossberg neural network systems are still quite limited. To the best of our knowledge, there is only one paper [35] devoted to the study of this extended stability concept for a class of bidirectional associative memory Cohen-Grossberg neural networks with time-varying delays. However, distributed delays, uncertain parameters and robust stability are not considered in this unique investigation.…”

“…In fact, impulses at variable instances are more realistic and include as a special case fixed moments of impulsive jumps [60]- [62]. To the best of the authors' knowledge, variable impulsive perturbations have been discussed for Cohen-Grossberg neural networks in the recent papers [35] and [63]. However, the research in [35] does not include robust stability analysis, and [63] is devoted to the stability of a single almost periodic solution with respect to the distance.…”

“…To the best of the authors' knowledge, variable impulsive perturbations have been discussed for Cohen-Grossberg neural networks in the recent papers [35] and [63]. However, the research in [35] does not include robust stability analysis, and [63] is devoted to the stability of a single almost periodic solution with respect to the distance. Both papers do not consider distributed delays.…”