Global dissipativity and adaptive synchronization for fractional‐order time‐delayed genetic regulatory networks

Abstract

This manuscript examines global dissipativity and synchronization criteria for time-delayed fractional-order gene regulatory networks (FGRNs). The Lyapunov stability theory is used to examine a class of FGRNs with delay arguments that are inspired by the integer-order delayed gene regulatory network model. Some sufficient criteria are established using the fractional-order comparison principle and stability theorem for fractional-order time-delayed systems to ensure the global dissipativity solution of FGRNs with both feedback regulation and translation time delays. Furthermore, for FGRNs, the global asymptotic synchronization condition is accomplished by constructing an adaptive delayed feedback control method for the master-slave system. Finally, two numerical examples are provided to demonstrate the applicability and superiority of the conclusions obtained.

Robust uniform stability criteria for fractional‐order gene regulatory networks with leakage delays

“…In, 31 the authors have analyzed the robust finite‐time stability for time‐varying delayed FOCTGRNs by means of generalized Gronwall–Belmann inequality. Very recently, the authors in Zhang et al 32 have derived the dissipativity and synchronization analysis of FOCTGRNs with both feedback regulation, and translation time delays based on fractional‐order comparison principle and fractional‐order Lyapunov direct approach. Besides, the author in 33 have analyzed the existence and finite‐time stability of FOCTGRNs with feedback regulation delay for two different order and , respectively based on some fractional‐order inequality techniques.…”