Stability-preserving discrete models for a class of continuous neural network models

Abstract

In the present world, neural networks have revolutionized technology and day-to-day life and helped us go to the next level of artificial intelligence. It is crucial to discretize the continuous dynamical neural network model while maintaining its qualitative characteristics in order to broaden the applications of this model further. The various continuous dynamical systems with one or two layers of neural networks are taken into account in this paper, and they are discretized using a novel non-finite difference approach. The investigation of continuous models and the subsequent derivation of discrete models lead to the establishment of findings on the stability of equilibrium at both local and global scales. The outcomes of the discrete models are frequently compared with those of their continuous equivalents. The non-standard finite difference technique that has been developed has been found to maintain the equilibrium and stability properties of the corresponding continuous systems. Numerical examples are used to explain and support the theoretical findings.