Lyapunov Approach for Almost Periodicity in Impulsive Gene Regulatory Networks of Fractional Order with Time-Varying Delays

Abstract

This paper investigates a class of fractional-order delayed impulsive gene regulatory networks (GRNs). The proposed model is an extension of some existing integer-order GRNs using fractional derivatives of Caputo type. The existence and uniqueness of an almost periodic state of the model are investigated and new criteria are established by the Lyapunov functions approach. The effects of time-varying delays and impulsive perturbations at fixed times on the almost periodicity are considered. In addition, sufficient conditions for the global Mittag–Leffler stability of the almost periodic solutions are proposed. To justify our findings a numerical example is also presented.

Exponential convergence in the mean-square sense of nonlocal stochastic almost automorphic genetic regulatory lattice networks

“…The research findings in this article extend and complement the works in literatures (Aouiti and Dridi, 2021; Ayachi, 2021, 2022; Duan et al, 2020; Stamova and Stamov, 2021; Zhang et al, 2020; Zhang and Xu, 2019).…”

“…However, almost no paper regards almost automorphic sequences of discrete-time stochastic gene regulatory lattice networks. Thus, the current work extends the works in papers (Aouiti and Dridi, 2021; Ayachi, 2021, 2022; Duan et al, 2020; Stamova and Stamov, 2021).…”

“…Therefore, gene regulatory networks are not only the basis for studying various phenomena in living organisms, but also offer a wide range of prospects for applications in systematic biology. In the previous decades, a number of literatures have been reported for gene regulatory networks, please refer Pasquini and Angeli (2021), Augier and Yabo (2022), Kim et al (2022), Hillerton et al (2022), Stamova and Stamov (2021), Padmaja and Balasubramaniam (2022), Stamov and Stamova (2021) and Qiao et al (2020). On the contrary, fractional calculus (Kilbas et al, 2006; Zhang and Xiong, 2020) is more than 300 years.…”

“…It allows us to characterize a more accurate representation of the problem than the traditional “integer order” approach. Fractional-order gene regulatory networks have played an exceedingly significant position in the evolution of systematic biology, as they provide an efficacious way to describe memory and genetic properties, refer Stamova and Stamov (2021), Padmaja and Balasubramaniam (2022), Stamov and Stamova (2021) and Qiao et al (2020). Padmaja and Balasubramaniam (2022) considered the H ∞ /passivity performance of fractional-order gene regulatory networks in the form of…”

“…For all the authors know, up to now, there are few papers focusing on the study of almost periodicity or automorphy to genetic regulatory networks in literatures (Aouiti and Dridi, 2021; Ayachi, 2021, 2022; Duan et al, 2020; Stamova and Stamov, 2021). Furthermore, almost no paper discusses almost automorphic oscillations of fractional-order stochastic gene regulatory networks with reaction diffusions, and we can observe that almost all of the existing findings are about the time variable.…”