Journal
MATHEMATICS
Volume 8, Issue 7, Pages -Publisher
MDPI
DOI: 10.3390/math8071082
Keywords
integral manifolds; Cohen-Grossberg-type neural networks; delays; reaction-diffusion terms; variable impulsive perturbations; boundedness; stability
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The present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen-Grossberg-type with reaction-diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based on the Lyapunov functions technique and Poincare-type inequality some new global stability criteria are also proposed in our research. In addition, we consider the case when the impulsive jumps are not realized at fixed instants. Instead, we investigate a system under variable impulsive perturbations. Finally, examples are given to demonstrate the efficiency and applicability of the obtained results.
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