On Synchronization Control Of Fractional-Order Complex Networks

Since fractional-order calculus can accurately describe individuals and dynamic evo-lution with memory and hereditary characteristics,it is of practical significance to intro-duce fractional-order calculus into complex networks to describe the memory and heredity of node dynamics.At present,there are already several results to analysis the synchro-nization and control of fractional-order complex networks,but the current work ignores the coupling and clustering expression characteristics of genetic networks.Besides,the reaction-diffusion phenomenon caused by the uneven distribution of protein and mRNA in cells is ignored,and the influence of the fractional order and complex-value character-istics of the system on the finite-time synchronization of the network is not considered.In view of this,based on pinning control,fractional-order adaptive control,impulsive con-trol,finite-time power-law control and other modern control means,this paper will use the theory of fractional-order differential equation,complex networks,complex function,matrix and other basic theories to discuss the cluster synchronization of fractional-order coupled genetic networks,exponential synchronization of fractional-order coupled genet-ic regulatory networks with reaction-diffusion terms and finite-time synchronization of fractional-order complex-variable complex networks respectivelyFirstly,the coupling and clustering expression of genes are considered,and a class of fractional-order coupled genetic regulatory network model is proposed.By establishing fractional-order inequality and designing pinning control strategy,some criteria of clus-ter synchronization for fractional-order networks are obtained,and some detailed pinning control schemes,including how to select the controlled nodes and how many nodes should be controlled,are provided.In addition,the fractional-order adaptive control strategy is designed for the feedback control gain to optimize the control cost.Finally,the corre-sponding numerical simulation is given to verify the synchronization condition and the effectiveness of the control strategyConsidering the diffusion phenomenon caused by the uneven distribution of protein and mRNA in cells,in the second part,reaction-diffusion terms are introduced into ge-netic networks,and the exponential synchronization of a kind of fractional-order coupled genetic regulatory networks with reaction-diffusion terms is discussed by using impulsive control strategy.Firstly,based on the Dirac function,the controlled networks are trans-formed into fractional-order impulsive differential systems.Then,by using the fractional-order impulsive differential inequality and the average impulsive interval method,the cri-teria for ensuring the exponential synchronization are established.Finally,a numerical example is given to verify the effectiveness of the theoretical resultsIn the third part,without dividing complex-variable networks into two subsystems with real values,the finite-time synchronization is considered for complex-valued dynam-ical networks with fractional order by means of the theory of complex-variable functions First of all,as a generalization of the real-valued sign function,the sign functions of complex-valued numbers and complex-valued vectors are introduced and some related inequalities are established.Under the sign function framework,two complex-valued control strategies are designed based on two different norms of complex numbers.Some synchronization criteria are derived and the settling times of synchronization are effec-tively estimated by developing fractional-order finite-time differential inequalities and utilizing the theory of complex-variable functions.The established theoretical results are demonstrated and the effect of the fractional order of the network model on the finite-time synchronization are revealed finally by providing some numerical simulations.