Impact of multiple time delays on bifurcation of a class of fractional nearest-neighbor coupled neural networks - Li, Weinan; Liao, Maoxin; Huang, Haoming; Xu, Changjin; Li, Bingbing (Nonlinear Analysis: Modelling and Control, 2024)
In this paper, the impacts of multiple time delays on bifurcation of a class of fractional nearest-neighbor coupled neural networks are considered. Firstly, the sum of time delays is selected as a parameter, and the fractional nearest-neighbor coupled neural network model is linearized to obtain the corresponding characteristic equation. Then, utilizing stability and bifurcation theory of fractional-order delay differential equations, we investigate the effect of time delays on the system’s stability and bifurcations. The results show that when the time lag exceeds the critical value, the system will lose stability and generate Hopf bifurcation. Finally, the correctness of the conclusions in this paper is verified through numerical simulation.
Keywords: nearest-neighbor coupled neural networks; fractional order; Hopf bifurcation; stability; delay