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

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.

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

Fractal and Fractional ◽

10.3390/fractalfract5040268 ◽

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.

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

Complexity ◽

10.1155/2020/2315272 ◽

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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Guaranteed Cost Control for Uncertain Gene Regulatory Networks with Interval Time-Varying Discrete Delays and Constant Distributed Delays

2020 39th Chinese Control Conference (CCC) ◽

10.23919/ccc50068.2020.9189156 ◽

2020 ◽

Author(s):

Zhiwei Zhang ◽

Heng Liu ◽

Xinyue Zhang ◽

Yantao Wang ◽

Xian Zhang

Keyword(s):

Gene Regulatory Networks ◽

Regulatory Networks ◽

Cost Control ◽

Guaranteed Cost Control ◽

Distributed Delays ◽

Time Varying ◽

Interval Time ◽

Guaranteed Cost ◽

Discrete Delays ◽

Gene Regulatory

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

International Journal of Biomathematics ◽

10.1142/s1793524519500670 ◽

2019 ◽

Vol 12 (06) ◽

pp. 1950067 ◽

Cited By ~ 3

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.

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Complex projection synchronization of fractional order uncertain complex-valued networks with time-varying coupling

Modern Physics Letters B ◽

10.1142/s0217984919503512 ◽

2019 ◽

Vol 33 (29) ◽

pp. 1950351 ◽

Cited By ~ 1

Author(s):

Dawei Ding ◽

Xiaolei Yao ◽

Hongwei Zhang

Keyword(s):

Fractional Order ◽

Coupling Strength ◽

Dynamic Networks ◽

Sufficient Conditions ◽

Feedback Gain ◽

Time Varying ◽

Order Complex ◽

Unknown Parameters ◽

Synchronization Problem ◽

Complex Valued

In this paper, the complex projection synchronization problem of fractional complex-valued dynamic networks is investigated. Considering the time-varying coupling and unknown parameters of the fractional order complex network, several decentralized adaptive strategies are designed to adjust the coupling strength and controller feedback gain in order to investigate the complex projection synchronization problem of the system. Moreover, based on the designed identification law, the uncertain parameters in the network can be estimated. Using adaptive law which balances the time-varying coupling strength and the feedback gain of the controller, some sufficient conditions are obtained for the complex projection synchronization of complex networks. Finally, numerical simulation examples are provided to illustrate the efficiency of the complex projection synchronization strategies of the fractional order complex dynamic networks.

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