Bifurcation Mechanism for Fractional-Order Three-Triangle Multi-delayed Neural Networks

• Published in: Neural processing letters Vol. 55; no. 5; pp. 6125 - 6151
• Main Authors: Xu, Changjin, Liu, Zixin, Li, Peiluan, Yan, Jinling, Yao, Lingyun
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2023; Springer Nature B.V
• Subjects: Artificial Intelligence; Calculus; Complex Systems; Computational Intelligence; Computer Science; Dynamical systems; Eigenvalues; Eigenvectors; Equilibrium; Hopf bifurcation; Investigations; Neural networks; Neurons; Stability; Time lag; Bifurcation diagram; Stability; Hopf bifurcation; Fractional-order three-triangle neural networks; Delay
• ISSN: 1370-4621; 1573-773X
• DOI: 10.1007/s11063-022-11130-y

This article is basically concerned with the stability and Hopf bifurcation problem of fractional-order three-triangle multi-delayed neural networks. Based on laplace transform, we obtain the characteristic equation of the considered fractional-order three-triangle multi-delayed neural networks. By discussing the distribution of the roots for the characteristic equation, the delay-independent stability condition and delay-induced bifurcation criterion are built. The research manifests that time delay is an important factor which affects the stability and the onset of Hopf bifurcation for fractional-order three-triangle multi-delayed neural networks. The computer simulation results and bifurcation figures are displayed to support the established main conclusions. The derived fruits of this article have great theoretical values in dominating neural networks.