Bifurcation Properties for Fractional Order Delayed BAM Neural Networks

In the past several decades, many papers involving the stability and Hopf bifurcation of delayed neural networks have been published. However, the results on the stability and Hopf bifurcation for fractional order neural networks with delays and fractional order neural networks with leakage delays are very rare. This paper is concerned with the stability and the existence of Hopf bifurcation of fractional order BAM neural networks with or without leakage delay. The Laplace transform, stability and bifurcation theory of fractional-order differential equations and Matlab software will be applied. The stability condition and the sufficient criterion of existence of Hopf bifurcation for fractional order BAM neural networks with delay (leakage delay) are established. It is found that when the sum of two delays (leakage delay) crosses a critical value, then a Hopf bifurcation will appear. The obtained results play an important role in designing neural networks. Also the derived results are new and enrich the bifurcation theory of fractional order delayed differential equations.

Automated summary

This paper focuses on the stability and Hopf bifurcation of fractional order BAM neural networks with or without leakage delay. By applying Laplace transform, stability and bifurcation theory of fractional-order differential equations and Matlab software, the study establishes the conditions and criteria for stability and the existence of Hopf bifurcation in these networks. The results have implications for neural network design and contribute to the bifurcation theory of fractional order delayed differential equations.