# Effect of leakage delay on Hopf bifurcation in a fractional BAM neural network

## TL;DR

This paper investigates how leakage delay influences Hopf bifurcation in a fractional BAM neural network, highlighting the critical role of delay in neural dynamics and employing sensitivity analysis to quantify its impact.

## Contribution

It introduces a novel analysis of leakage delay effects on Hopf bifurcation in fractional neural networks, combining bifurcation theory with sensitivity assessment methods.

## Key findings

- Hopf bifurcation occurs at critical delay values
- Leakage delay significantly affects bifurcation amplitude
- Numerical examples confirm theoretical predictions

## Abstract

Recently, the influence of leakage delay on the dynamics of integer-order neural networks has been investigated extensively. It has been confirmed that fractional calculus can depict the memory and hereditary attributes of neural networks more accurately. In this paper, we study the existence of Hopf bifurcation in a six-neuron fractional bidirectional associative memory (BAM) neural network with leakage delay. By selecting two appropriate bifurcation parameters and analyzing corresponding characteristic equations, it is verified that the delayed fractional neural network generates a Hopf bifurcation when the bifurcation parameters pass through some critical values. In order to measure how much impact of leakage delay on Hopf bifurcation, sensitivity analysis methods, such as scatter plots and partial rank correlation coefficients (PRCCs), are introduced to assess the sensitivity of bifurcation amplitudes to leakage delay. Numerical examples are carried out to illustrate the theoretical results and help us gain an insight into the effect of leakage delay vividly.