Bifurcation control of a novel fractional-order gene regulatory network with incommensurate order and time delay

Gene regulatory networks play an extremely important role in human life activities. This paper presents a novel fractional-order gene regulatory network model (NFGRNM). The model employs incommensurate fractional orders and introduces time delay arising from the binding of miRNAs to RNA. Time delay often triggers instability such as oscillation and bifurcation, so in this paper we introduce a generalized hybrid control to control the unstable dynamical behavior induced by time delay. First we derive the NFGRNM using fractional order theory, after which the equilibrium point of the network model is calculated. Next, a systematic dynamics analysis of the NFGRNM is performed to derive sufficient conditions to generate the Hopf bifurcation. Most importantly, we introduce the extended hybrid control for the periodic oscillations generated by the time delay in the NFGRNM. Finally, numerical simulation results show that the order of the fractional order can have a great impact on the dynamical behavior of the network model and that the hybrid control has a significant role in delaying (or advancing) the Hopf bifurcation. Since infectious diseases such as SARS-Cov-2, influenza A, and HIV are still prevalent today, the study of gene regulatory networks not only promotes the study of the dynamics of complex networks but also has profound implications for the study of virus transmission in the host and various life activities in humans.