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Multi-parametric bifurcations of a fractional neural network with multiple delays and inertial terms

  • 0School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China.
Neural Networks : the Official Journal of the International Neural Network Society +

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December 30, 2025

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December 30, 2025

View abstract on PubMed

Summary

This summary is machine-generated.

This study investigates Hopf bifurcation in fractional-order neural networks with delays and inertial terms. Findings show that time delay, fractional order, and inertial parameters enhance system stability.

Area Of Science

  • Dynamical Systems
  • Computational Neuroscience
  • Fractional Calculus

Background

  • Neural networks with memory and inertial effects exhibit complex dynamics.
  • Hopf bifurcation is a critical phenomenon in analyzing system stability.
  • Fractional-order derivatives offer a more realistic model for neural networks.

Purpose Of The Study

  • To systematically investigate the Hopf bifurcation in Caputo fractional-order delayed neural networks with inertial terms.
  • To analyze the influence of time delays, fractional order, and inertial parameters on system stability.
  • To derive conditions for bifurcation onset and identify parameters that enhance stability.

Main Methods

  • Analysis of induction conditions for delay-induced bifurcation.
  • Utilizing degree reduction of transcendental terms and implicit function array to find critical values.
  • Extraction of bifurcation conditions for fractional order and inertial parameters based on quadratic relationships.
  • Numerical simulations to validate theoretical findings.

Main Results

  • Established conditions for Hopf bifurcation induced by time delay.
  • Determined critical values of the characteristic equation using two distinct methods.
  • Derived conditions for bifurcation related to fractional order and inertial parameters.
  • Demonstrated that reducing these parameters expands the stability region.

Conclusions

  • Time delay, fractional order, and inertial parameters significantly impact the stability of fractional-order delayed neural networks.
  • These parameters can be tuned to enlarge the stability region, leading to improved operational stability.
  • The findings provide valuable insights for designing more robust and stable neural network systems.

Keywords:

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