Global stability analysis of fractional-order gene regulatory networks with time delay

Abstract

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

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

“…In addition, it complements the almost periodicity results in [48] obtained by the Cauchy matrix estimations and the theory of contracting operators in Banach spaces, using the Lyapunov function approach. In fact, the advantages of the Lyapunov method are used in the qualitative investigation of numerous problems [14,[16][17][18]23,26,27,[49][50][51], including fractional-order GRNs [28][29][30][31][32][33][34].…”

“…A type of fractional-order GRNs has been introduced in [30] to synchronize at finite-time point by designing feedback controls. A global stability analysis of fractionalorder GRNs with time delay has been conducted in [31]. The paper [32] is devoted to the global uniform asymptotical stability of fractional GRNs with time-varying delays and structured uncertainties.…”

“…In this paper, we will apply the fractional Lyapunov strategy to investigate the existence and stability of almost periodic states for a class of fractional-order GRNs. Indeed, the Lyapunov method is a very powerful technique that is applied intensively by many researches in the investigations of the qualitative properties of fractional-order problems and impulsive control problems [14,[16][17][18]23,26,27,[49][50][51], including fractional-order GRNs [28][29][30][31][32][33][34].…”

Stability of Gene Regulatory Networks Modeled by Generalized Proportional Caputo Fractional Differential Equations

“…This result is applied by many authors to study the stability of various types of Caputo fractional differential equations and models. For example, this equality is applied in the proof of global Mittag-Leffler stability for fractional-order gene regulatory networks in [3], and to study global uniform asymptotical stability for fractional-order gene regulatory networks with delays in [4,18]. Unfortunately, this equality is not satisfied for all continuously differentiable functions, and we will demonstrate this with an example.…”

Global Synchronization and Anti-Synchronization of Fractional-Order Complex-Valued Gene Regulatory Networks With Time-Varying Delays

“…Jiang et al [17] considered the finite-time synchronization of integer-order GRNs without time delays, and established some sufficient conditions for finite-time stochastic synchronization by designing a continuous finite-time controller. Due to slow biochemical processes such as gene transcription, translation and transportation, time delays are omnipresent in GRNs [4], [9], [11], [14], [15], [38]- [40]. Qiao et al [11] established some sufficient conditions of finite-time synchronization for fractional-order GRNs with constant time delay by designing respectively the state feedback controller and the adaptive controller.…”