Symmetrical Impulsive Inertial Neural Networks with Unpredictable and Poisson-Stable Oscillations

Abstract

This paper explores the novel concept of discontinuous unpredictable and Poisson-stable motions within impulsive inertial neural networks. The primary focus is on a specific neural network architecture where impulses mimic the structure of the original model, that is, continuous and discrete parts are symmetrical. This unique modeling decision aligns with the real-world behavior of systems, where voltage typically remains smooth and continuous but may exhibit sudden changes due to various factors such as switches, sudden loads, or faults. The paper introduces the representation of these abrupt voltage transitions as discontinuous derivatives, providing a more accurate depiction of real-world scenarios. Thus, the focus of the research is a model, exceptional in its generality. To study Poisson stability, the method of included intervals is extended for discontinuous functions and B-topology. The theoretical findings are substantiated with numerical examples, demonstrating the practical feasibility of the proposed model.