Abstract
This paper presents the analytical and numerical investigation on the global synchronization and anti-synchronization for a class of drive-response systems of fractional-order complex-valued gene regulatory networks with time-varying delays (DFGRNs). In our design, two kinds of adaptive feedback controllers are used to synchronize and anti-synchronize the proposed drive-response systems, and some sufficient conditions on the global asymptotical synchronization and anti-synchronization are given with the methods of the fractional Lyapunov-like functions and the fractional-order inequalities. In the numerical simulations, two minimum “estimated time”, T 1 and T 2 , are computed to achieve the synchronization and anti-synchronization. We find that T 1 and T 2 increase with the decreasing of the fractional order of DFGRNs.
Highlights
Genetic regulatory networks (GRNs) are fundamental and important biological networks that describe the interaction functions in gene expressions between DNAs, RNAs, proteins and small molecules in an organism [1]–[5]
According to our knowledge, few researches have been given to the synchronization and antisynchronization of fractional-order complex-valued GRNs with time-varying delays
MAIN RESULTS First, we consider the global synchronization of DFGRNs based on the adaptive feedback controller
Summary
Genetic regulatory networks (GRNs) are fundamental and important biological networks that describe the interaction functions in gene expressions between DNAs, RNAs, proteins and small molecules in an organism [1]–[5]. In [18]–[20], the authors pointed out that fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various processes Taking into account these facts, the incorporation of a memory term into a neural network model is an extremely important improvement [21]. Bao et al [27] investigated the synchronization for fractional-order complex-valued neural networks with constant time delay and obtained the sufficient conditions of synchronization by using linear delay feedback control. 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. According to our knowledge, few researches have been given to the synchronization and antisynchronization of fractional-order complex-valued GRNs with time-varying delays.
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