Local Bifurcation Analysis of a Fractional-Order Dynamic Model of Genetic Regulatory Networks with Delays

In this paper, we propose a delayed fractional-order gene regulatory network model. Firstly, the sum of delays is chosen as the bifurcation parameter, and the conditions of the existence for Hopf bifurcations are achieved through analyzing its characteristic equation. Secondly, it is shown that the fractional order can be effectively manipulated to control the dynamics of such network, and the stability domain can be changed with different fractional orders. The fractional-order genetic network can generate a Hopf bifurcation (oscillation appears) as the sum of delays passes through some critical values. Therefore, we can achieve some desirable dynamical behaviors by choosing the appropriate fractional order. Finally, numerical simulations are carried out to illustrate the validity of our theoretical analysis.