Generalization of neuron network model with delay feedback

TL;DR

This paper introduces a generalized delayed neural network model with positive feedback and neuron history, analyzing stability and zero root multiplicity, and extending models to N neurons.

Contribution

It develops new delayed neural network models in various dimensions, analyzes zero root multiplicity, and generalizes the neural network to N neurons with a comprehensive characteristic equation.

Findings

Zero root can have multiplicity two under certain conditions

Conditions for the existence of zero root are established

General form of Jacobian and characteristic equation for N neurons

Abstract

We present generalized delayed neural network (DNN) model with positive delay feedback and neuron history. The local stability analysis around trivial local equilibria of delayed neural networks has applied and determine the conditions for the existence of zero root. We develop few innovative delayed neural network models in different dimensions through transformation and extension of some existing models. We found that zero root can have multiplicity two under certain conditions. We further show how the characteristic equation can have zero root and its multiplicity is dependent on the conditions undertaken. Finally, we generalize the neural network of $N$ neurons through which we determine the general form of Jacobian of the linear form and corresponding characteristic equation of the system.