Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer's rule

This article is dedicated to reseaching the bifurcations of a fractional-order neural network (FONN) with nonidentical self-connection and comunication delays. In accordance with eigenvalue analysis, we apply Cramer's rule to ingeniously calculate the specific value of the bifurcation point of an equation set with quartic transcendence term. It is noteworthy that the method proposed in this article is more concise than the existing methods for solving higher-order transcendental terms, and has a certain degree of generalization, which can be applied to the case involving n degree transcendental terms. Furthermore, it detects that the devised FONN can ameliorate dramatically the stability attributions in comparison with its integer-order counterpart. This article ultimately provides two experimental fruits for bifurcation caused by different delays to underpin the correctness of the developed methodology.