Dynamics of fractional-order neural networks with discrete and distributed delays

Lingzhi Si, Min Xiao, Min Xiao, Guoping Jiang, Zunshui Cheng, Qiankun Song, Jinde Cao
2019 IEEE Access  
This paper is concerned with the stability and Hopf bifurcation of fractional-order neural networks with discrete and distributed delays. The novelty of this paper is to take into account the discrete time delay and the distributed time delay for fractional-order systems. By introducing two virtual neurons to the original network, a new four-neuron network only involving discrete delays is formed. The sum of discrete delays is adopted as the bifurcation parameter to demonstrate the existence of
more » ... Hopf bifurcation. It is found that the critical value of bifurcation can be effectively manipulated by choosing appropriate system parameters and order. Finally, numerical simulations are executed to substantiate the theoretical results and describe the relationships between the parameters and the onset of bifurcation. INDEX TERMS Stability, Hopf bifurcation, discrete delay, distributed delay, fractional-order neural networks.
doi:10.1109/access.2019.2946790 fatcat:jievokmqrbewjmnq4lldfi473i