Stabilization Of Boolean Control Networks With Stochastic Impulses

Motivated by the Human Genome Project,systems biological is emerging.Therefore,a number of models for studying biological networks have emerged,including linear models,differential equations,neural networks,and Boolean networks.Boolean networks,first introduced by Kauffman in 1969,because of its simple structure,have become powerful tools for describing,analyzing,and simulating cellular networks.During the gene expression,evolutionary processes in biological networks are often subject to instantaneous disturbances and abrupt changes at certain instants,which may be caused by switching phenomena,or other sudden changes,i.e.,they exhibit impulsive effects.Because of the mutability of the external environment,the occurrence of impulses are usually randomness,we call this stochastic impulses.As one of the important behaviors of dynamic networks,stability has been widely studied.Global stabilization of a Boolean network usually refers to the existence of a moment when all states in the whole space reach the same state.However,there are still some networks where all states arrive at and stabilization in the same set,which is called Boolean control network set stabilization.Therefore,the stabilization and set stabilization of Boolean control networks with stochastic impulses are subjects worth studying.This thesis constructs Boolean control networks with stochastic impulses,and uses the left semi-tensor product transform the difference equations into algebraic forms to study the stabilization and set stabilization of Boolean control networks with stochastic impulses.Using MATLAB to calculate biological examples to verify the correctness of the theory.The main contents of the paper are described as follows:First,after learning the models in the field of Boolean networks,on the basis of the currently widely studies,stochastic impulses model is added to build Boolean control networks with stochastic impulses,so as to better simulate the real biological system.Second,the global stabilization of Boolean control networks with stochastic impulses is studied.Based on the final state of the whole network,the iterative process of the network is analyzed in reverse.A sufficient condition is given to judge whether a network can achieve global stabilization.In addition,the proof of the theorem gives the setting of impulses strategies and feedback control.The research results are applied to the global stabilization of probabilistic Boolean control networks with stochastic impulses.Third,the set stabilization of Boolean control networks and the probability Boolean control networks with stochastic impulses is studied based on invariant subset.Using the idea of global stabilization,the basic symbols are redefined,impulses strategies and feedback control are modified to give the sufficient and necessary condition.Then,the results are extended to probabilistic Boolean control networks with stochastic impulses.Finally,two numerical examples are given and calculated by MATLAB software to verify the feasibility of the proposed control strategy,the validity of the global stability and set stability results.