Investigation of Delay-Induced Hopf Bifurcation in a Fractional Neutral-Type Neural Network
Year: 2025
Type: article
Abstract: This paper investigates stability switches induced by Hopf bifurcation in a fractional three-neuron network that incorporates both neutral time delay and communication delay, as well as a general structure. Initially, we simplified the characteristic equation by eliminating trigonometric terms associated with purely imaginary roots, enabling us to derive the Hopf bifurcation conditions for communication delay while treating the neutral time delay as a constant. The results reveal that communication delay can drive a stable equilibrium into instability once it exceeds the Hopf bifurcation threshold. Furthermore, we performed a sensitivity analysis to identify the fractional order and neutral delay as the two most sensitive parameters influencing the bifurcation value for the illustrative example. Notably, in contrast to neural networks with only retarded delays, our numerical observations show that the Hopf bifurcation curve is non-monotonic, highlighting that the neural network with a fixed communication delay can exhibit stability switches and eventually stabilize as the neutral delay increases.
Source: Fractal and Fractional
Authors: Shuai Li, Xinyu Song, Chengdai Huang
Institution: Xinyang Normal University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
OpenAlex ID: W4408647889