Stability and bifurcations in fractional-order gene regulatory networks

2022 ◽  
Vol 421 ◽  
pp. 126916
Author(s):  
Eva Kaslik ◽  
Ileana Rodica Rădulescu
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Gene Regulatory ◽  
Stability And Bifurcations

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

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

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.

scholarly journals Global uniform asymptotical stability for fractional-order gene regulatory networks with time-varying delays and structured uncertainties

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Time Varying ◽  
The Novel ◽  
Razumikhin Technique ◽  
Gene Regulatory ◽  
The Stability

AbstractIn this paper, we investigate a class of fractional-order gene regulatory networks with time-varying delays and structured uncertainties (UDFGRNs). First, we deduce the existence and uniqueness of the equilibrium for the UDFGRNs by using the contraction mapping principle. Next, we derive a novel global uniform asymptotic stability criterion of the UDFGRNs by using a Lyapunov function and the Razumikhin technique, and the conditions relating to the criterion depend on the fractional order of the UDFGRNs. Finally, we provide two numerical simulation examples to demonstrate the correctness and usefulness of the novel stability conditions. One of the most interesting findings is that the structured uncertainties indeed have an impact on the stability of the system.

scholarly journals A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks

2021 ◽  
Vol 6 (5) ◽  
pp. 4526-4555
Author(s):  
Pratap Anbalagan ◽  
◽  
Evren Hincal ◽  
Raja Ramachandran ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Gene Regulatory

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

2021 ◽  
Vol 5 (4) ◽  
pp. 268
Author(s):  
Ivanka Stamova ◽  
Gani Stamov
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Sufficient Conditions ◽  
Almost Periodicity ◽  
Time Varying ◽  
Almost Periodic ◽  
Proposed Model ◽  
Periodic State ◽  
Gene Regulatory

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.

scholarly journals Finite-Time Stability of Fractional-Order Time-Varying Delays Gene Regulatory Networks with Structured Uncertainties and Controllers

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Finite Time ◽  
Regulatory Networks ◽  
State Feedback ◽  
Time Varying ◽  
Time Stability ◽  
Feedback Controllers ◽  
Finite Time Stability ◽  
Gene Regulatory

In this paper, we investigate a class of fractional-order time-varying delays gene regulatory networks with structured uncertainties and controllers (DFGRNs). Our contributions lie in three aspects: first, a necessary and sufficient condition on the existence of the solution for the DFGRNs is given by using the properties of the Riemann–Liouville fractional derivative and Caputo’s fractional derivative; second, the unique solution of the DFGRNs is proved under given initial function and certain condition; third, some novel sufficient conditions on finite-time stability of the DFGRNs are established by using a generalized Gronwall inequality and norm technique, and some conclusions on the finite-time stability of the DFGRNs with memory state-feedback controllers are reached, and those conditions and conclusions depend on the fractional order of the DFGRNs. One of the most interesting findings is that the “estimated time” of the finite-time stability is indeed related to the structured uncertainties, state-feedback controllers, time delays, and the fractional order of the system.

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