Stability of neural networks with non-instantaneous impulses and supremum
Snezhana G. Hristova, Krasimira Ivanova, Todor Kostadinov · AIP conference proceedings · 2019
We consider the Hopfield’s graded response neural network in the case when the neurons are subject to a certain impulsive state displacement at fixed moments and the duration of this displacement is not negligible small (they are known as non-instantaneous impulses). We examine the case when the present state of any neuron depends on its maximum value over a past time variable interval. The self-regulating parameters of all units as well as the functions of the connection between two neurons in the network are time varying. The stability of the equilibrium of the model is studied. The study is based on the application of Lyapunov functions. The obtained sufficient conditions are explicitly expressed in terms of the parameters of the system and hence they are easily verifiable.