Effects Of Impulses On Dynamics Of Neural Networks And Viruses Propagation

The impulsive neural networks exhibiting the rich dynamical behaviors are a relatively important part of the impulsive differential systems.It is well known that impulsive phenomena are widespread,especially in practical neural networks,where impulsive perturbations are likely to emerge since the states of neural networks are changed abruptly at certain moments of time.The impulsive neural networks are always the focus of attention.In recent years,the neural networks with state-dependent impulses have also attracted much attention.In addition,in the efforts of scholars,a series of significative results for the switching neural networks have also been obtained.There are many applications of impulse in real life,for example,the spread of network viruses can be effectively prohibited by using impulsive vaccination and impulsive detoxication.In this paper,by means of B-equivalence method,the Lyapunov function and some analysis techniques,we investigate the stability issues of several classes of state-dependent impulsive neural networks,and we study the dynamical properties of computer viruses propagation models with impulsive vaccination,impulsive detoxication and saturation effect by the comparison theorem and bifurcation theory in impulsive differential equations.The main contents are as follows:Firstly,we investigate the effects of state-dependent impulses on global exponential stability of Cohen-Grossberg neural networks(CGNN)by using B-equivalence method and the Lyapunov function.Under certain conditions,we show that the state-dependent impulsive systems can be reduced to the fixed-time ones;and that impulsive CGNN will remain stability property of continuous subsystem even if the impulses are of somewhat destabilizing,and that stabilizing impulses can stabilize the unstable continuous subsystem at its equilibrium points.And then the stability criteria of the considered CGNN in two cases are obtained.Secondly,We discuss the impacts of state-dependent impulses on global stability of switching Hopfield neural networks(HNN)by means of B-equivalence method,the switching Lyapunov function and linear matrix inequality.Under certain conditions,we show that the state-dependent impulsive switching systems can be reduced to the fixedtime ones,and that the stability of corresponding comparison system implies the same stability of the considered system.On this basis,a novel stability criterion for the considered HNN is established.Thirdly,by use of B-equivalence method,the switching Lyapunov function and some analysis techniques,we investigate the global stability of switching Cohen-Grossberg neural networks with state-dependent impulses.Under certain conditions,the state-dependent impulsive switching systems can be reduced to the fixed-time ones.Furthermore,by using the proposed comparison system,a stability criterion for the considered CGNN is established.Finally,two numerical examples are provided to illustrate the efficiency of the theoretical results.Fourthly,we investigate the dynamical behavior of a new computer virus propagation model with impulsive vaccination and saturation effect by using the comparison theorem and bifurcation theory in impulsive differential equations.It aims to reveal how the impulsive vaccination affects the spread of electronic viruses.And some effective strategies for inhibiting network virus prevalence are suggested based on a parameter analysis for the model.Finally,some numerical examples also justify the proposed model.Lastly,by the comparison theorem and bifurcation theory in impulsive differential equations,we discuss the dynamical properties of a SIRS computer virus propagation model with impulsive detoxication and saturation effect.We get that the dynamical properties of the model is relating to the basic reproduction ratio.On this basis,some feasible measures for controlling network virus diffusion have been advised.