Hopf Bifurcation of Four-Dimensional Fractional-Order Complex-Valued Neural Network

This article explores stability and bifurcation issues within a four-dimensional fractional-order complex-valued neural network (FOCVNN) incorporating time-delay. By utilizing the time-delay as a bifurcation parameter, the study delves into the network's dynamic behavior, examining local asymptotic stability and Hopf bifurcation, calculate the system of equations containing four transcendental terms using Cramer's law to obtain the value of the bifurcation point, while also establishing the conditions for bifurcation occurrence. The theoretical findings are subsequently validated through numerical simulations.