Synchronization in Finite Time for Nabla Discrete Fractional Delayed Gene Regulatory Networks

Research on gene regulatory networks with integer and fractional orders has been widely conducted at various levels. However, there are still gaps in the study of discrete fractional-order gene regulatory networks. Therefore, this paper fills this gap by investigating the synchronization in finite time for nabla discrete fractional-order delayed gene regulatory networks (NDFGRNs). Firstly, adaptive control and feedback control are designed. Secondly, the control theory and fractional Lyapunov direct method are used to obtain sufficient conditions to realize the synchronization of gene regulatory network model in finite time, and the set time of synchronization is estimated according to the system parameters and control gain. Finally, a numerical example is given to verify the validity and feasibility of the theoretical results.