Full Text: PDF
DOI: 10.23952/jnfa.2026.14
Received December 4, 2025; Accepted March 2, 2026; Published May 25, 2026
Abstract. Fractional-order neutral-type recurrent neural networks (FONTRNNs) hold promise for dynamic modeling, yet fixed neutral term order in existing studies restricts regulation flexibility. This paper proposes a four-neuron FONTRNN with independently tunable neutral term order. By decoupling the characteristic equation into trigonometric-variable linear systems, we derive explicit delay-dependent stability criteria and Hopf bifurcation points via Cramer’s rule. Notably, an extended bifurcation framework is developed by treating the neutral term order as the bifurcation parameter, with critical values solved through implicit function curve intersection. Numerical simulations verify that reducing the derivative order consistently stabilizes the system, while adjusting the neutral term order enhances or weakens stability depending on parameter configurations.
How to Cite this Article:
H. Xu, C. Huang, H. Liu, L. Zhou, Delay and neutral-term order-regulated stability in four-neuron fractional-order recurrent neural networks, J. Nonlinear Funct. Anal. 2026 (2026) 14.