Dynamics Analysis Of Fractional-order Gene Regulatory Neural Networks With Time Delay

Fractional calculus is an extension of integral calculus.Compared with integral-order sys-tem,fractional-order system has memory and genetic characteristics,which describes complex natural phenomena more accurately.The combination of gene regulatory networks model and fractional calculus theory can effectively describe the interaction between DNA,RNA and pro-tein molecules.Therefore,exploring the dynamic behavior of fractional-order gene regulatory networks is helpful to understand the mechanism of gene interaction and further explain the complex life activities.This paper investigates the dynamic behavior of fractional-order gene regulatory networks with time delay,which is divided into three parts:firstly,the existence and uniqueness of the equilibrium point of fractional-order gene regulatory networks with time delay is proved by using the principle of compression mapping and fixed point theorem.Secondly,some sufficien-t conditions for finite-time synchronization of fractional-order gene regulatory networks with time delay are derived based on two kinds of different control techniques and fractional Lya-punov function approach,and the corresponding setting time is estimated.And some numerical examples are given to demonstrate the effectiveness of the theoretical results.Finally,we take the time delay as the bifurcation parameter,and analyze the characteristic equation to obtain the sufficient conditions of the stability and Hopf bifurcation for the four-dimensional fractional-order gene regulatory networks with time delay,and the effect of linear feedback control on the bifurcation point of the system.And some numerical examples are given to demonstrate the effectiveness of the theoretical results.