A Fractional-Order Multi-Delayed Bicyclic Crossed Neural Network: Stability, Bifurcation, and Numerical Solution

Abstract

In this paper, we propose a fractional-order bicyclic crossed neural network (NN) with multiple time delays consisting of two sharing neurons between rings. The given fractional-order NN is defined in terms of the Caputo fractional derivatives. We prove boundedness and the existence of a unique solution for the proposed NN. We do the stability and the onset of Hopf bifurcation analyses by converting the proposed multiple-delayed NN into a single-delay NN. Later, we numerically solve the proposed NN with the help of the L1 predictor-corrector algorithm and justify the theoretical results with graphical simulations. We explore that the time delay and the order of the derivative both influence the stability and bifurcation of the fractional-order NN. The proposed fractional-order NN is a unique multi-delayed bicyclic crossover NN that has two sharing neurons between rings. Such ring structure appropriately mimics the information transmission process within intricate NNs.