一类具脉冲和垂直传染的传染病模型的一致持续生存

本文建立了一类具脉冲和垂直传染的传染病模型,应用脉冲微分议程周期解的全局稳定性、比较原理和分析方法,得到了该模型一致持续生存的充分条件,通过结果可以帮助我们了解,注射疫苗的周期T和注射比例P与疾病控制的联系。

The Global Solutions of Impulsive Retarded Functional Differential Equations

In this paper, we present some results on the existence of the golbal solutions of nonlinear impulsive retarded functional differential equations.

The Existence of Solutions of Three-point Boundary Value Problems for Second Order Impulsive Differential Equation

We study the existence of solutions to the second order three-point boundary value problem：{x″（t）＋f（t,x（t）,x′（t））=0,t≠ti,△x（ti）=Ii（x（ti）,x′（ti））,i=1,2,…,k,△x′（ti）=Ji（x（ti）,x′（t））,i=1,2,…,k,x（0）=0=x（1）-αx（η）,where 0〈η〈1,α∈R,and f：[0,1]×R×R→R,Ii：R×R→R,Ji：R×R→R（i=1,2,…,k）are continuous. Our results is new and different from previous results. In particular, we obtain the Green function of the problem, which makes the problem simpler.

On the Existence of Positive Solutions for Impulsive Neutral Differential Equations

Aim To investigate the existence of positive solutions for impulsive neutral differential equations. Methods The Banach contraction principle was used to establish our results. Results and Conclusion The results of the existence of positive solutions for impulsive neutral differential equations are obtained.

Asymptotical p-Moment Stability of Stochastic Impulsive Differential Equations and Its Application in Impulsive Control

In this paper, the asymptotical p-moment stabifity of stochastic impulsive differential equations is studied, and a comparison theory to ensure the asymptotieal p-moment stability for trivial solution of this system is established, from which we can find out whether a stochastic impulsive differential system is stable just from a deterministic comparison system. As an application of this theory, we control the chaos of stochastic Chen system using impulsive method, and a stable region is deduced too. Finally, numerical simulations verify the feasibility of our method.

Permanence and Periodic Solution of an Impulsive Delay Two-prey One-predator System with Variable Coefficients

two-prey one-predator system with a special Holling-Ⅱ functional response is discussed. That w-periodic solution of the predator extinction is global asymptotically stable is proved by some new methods. Furthermore, by the comparison theorem of impulsive differential equation, the sufficient conditions are derived for the permanence and the existence of periodic solution of the system.

A Boundary Value Problem for Second Order Functional Differential Equations with Impulses

Aim To investigate the boundary value problem for second order functional differentiai equations with impulses. Methods The fixed point principle was used to establish our results. Results and Conclusion The results of the esistence, the uniqueness and the continuous dependence on aprameter of soiutions of the boundary value problems for second order functional differential equations with impulses are obtained.

Eigenvalue of a Class of Impulsive Differential Equation with BVPs

Consider the following equations：{λx＂（t）＋f（t,x（t））=0,t≠tiΔλx（ti）=Ii（x（ti））,i=1,2,…,kΔλx（ti）=Li（x（ti））,i=1,2,…,kx＇（0）=0=x（1）-αx（η）.Where 0 〈 η〈 1,0 〈 α 〈 1, and f ： [0,1] × [0, ∞） → [0, ∞）, Ii,Li ： [0, ∞） → R, （i = 1, 2,…, k） are continuous functions. We prove the existence of eigenvalues for the problem under a weaker condition, moreover we do not require the monotonicity of the impulsive functions.

Oscillation Criteria for Second-order Half-linear Impulsive Differential Equations with Damping

By employing the inequality of [8] and a positive continuous function g（t）, t[t0, ＋∞）, oscillation criteria for the second-order half-linear impulsive differential equ-ations with damping are established. Our results generalize and improve some known ones.

Initial Value Problems for Second Order Impulsive Integro-Differential Equation in Banach Spaces

By an established comparison result and using the upper and lower solutions,one sufficient condition of existence of minimal and maximal solutions to initial value problem for second order impulsive integro-differential equation in Banach spaces is obtained and the related results are essentially improved.At the same time, another sufficient condition of existence of minimal and maximal solutions based on the Kuratowski measure of noncompactness is given.

A COMPUTER-AIDED UNIFIED APPROACH TO MODELING PWM AND RESONANT CONVERTERS

This letter puts forward a method of modeling for the steady-state and small signal dynamic analysis on PWM, quasi-resonant and series/(parallel) resonant switching converters based on pulse-waveform integral approach. As an example, PWM and quasi-resonant converters are used to discuss the principle of the approach. The results are compared with those in the relative literatures. Computer aided analysis are made to confirm the correctness.

Oscillation of Nonlinear Impulsive Delay Hyperbolic Partial Differential Equations

In this paper,by making use of the calculous technique and some results of the impulsive differential inequality,oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated.Sufficient conditions for oscillations of such equations are obtained.

Microwave-Controlled Light-Pulse Propagation in a Driven A-Type Atomic System with Two-Folded Levels

The temporal and spatial dynamics of one weak probe laser pulse, propagating through a A-type atomic medium with two-folded levels under the resonant excitation of one microwave driving field and one strong control field, is investigated in this paper. By numerically solving coupled Bloch-Maxwell equations, it is found that, in the absence of the microwave driving field, the atomic medium is transparent to the probe pulse at line center, which propagates over sufficiently long distances. By contrast, when the microwave driving field is applied, the probe pulse at line center can be rapidly absorbed on propagation. This substantial reduction of probe transmittance caused by the microwave driving field may lead to potential applications in designing a new kind of optical switching.

Positive Solutions for Second Order Impulsive Differential Equations with Dependence on First Order Derivative

We study positive solutions for second order three-point boundary value problem：{″（t）＋f（t,x（t）,x＇（t））=0,t≠ti△x（ti）=Ii（x（ti）,x＇（ti））,i=1,2,3,…,k△x＇（ti）=Ji（x（ti）,x＇（t））,x（0）=0=x（1）-αx（η）,where 0〈η〈1,0〈α〈1,and f：[0,1]×（0,∞）×R→[0,∞）,Ii：[0,∞）×R→R,Ji：[0,∞）×R→R,（i=1,2,…,k）are continuous. Based on a new extension of Krasnoselskii fixed-point theorem （which was established by Guo Yan-ping and GE Wei-gao, the existence of positive solutions for the boundary value problems is obtained. In particular, we obtain the Green function of the problem, which makes the problem simpler.

On Existence and Uniqueness of Random Impulsive Differential Equations

This paper studies existence and uniqueness for random impulsive differential equations.The authors first generalize a random fixed point theorem of Schaefer's type.Then the authors shall rely on the generalized Schaefer's type random fixed point theorem to discuss the existence of the system.In addition,the authors study the existence and uniqueness of random impulsive differential equations by applying random Banach fixed point theorem and obtain some less conservative results.Finally,an example is given to illustrate the effectiveness of the results.

On generalized impulsive piecewise constant delay differential equations

A variation of parameters formula with Green function type and Gronwall type integral inequality are proved for impulsive differential equations involving piecewise constant delay of generalized type. Some results for piecewise constant linear and nonlinear delay differential equations with impulsive effects are obtained.They include existence and uniqueness theorems, a variation of parameters formula, integral inequalities, the oscillation property and some applications.

OSCILLATION AND GLOBAL ATTRACTIVITY OF IMPULSIVE PERIODIC DELAY RESPIRATORY DYNAMICS MODEL

This paper studies the nonlinear delay impulsive respiratory dynamics model. The model describes the sudden changes of the concentration of CO2 in the blood of the mammal. It is proved that the model has a unique positive periodic solution. Somesufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivityof the periodic solution are obtained.

Dynamics on tumor immunotherapy model with periodic impulsive infusion

A periodic pulse differential equation model of tumor immunotherapy is established by considering the periodic and transient behavior of infusing immune cells. Using comparison theorem and Floquet multiplier theory of the impulsive differential equation, the boundedness of the model solution, the existence and stability of the free-tumor periodic solution are given. Furthermore, the persistence of the system is analyzed. Numerical simulations are carried to confirm the main theorems.

Difference Scheme for Hyperbolic Heat Conduction Equation with Pulsed Heating Boundary

In this paper, the authors have analyzed the second-order hyperbolic differential equation with pulsed heating boundary, and tried to solve this kind of equation with numerical method. After analyzing the error of the difference scheme and comparing the numerical results with the theoretical results, the authors present some examples to show how the thermal wave propagates in materials. By analyzing the calculation results, the conditions to observe the thermal wave phenomena in the laboratory are conferred. Finally the heat transfer in a complex combined structure is calculated with this method. The result is quite different from the calculated result from the parabolic heat conduction equation.

The effect of vaccination to dendritic cell and immune cell interaction in HIV disease progression

In this research paper, our main objective is to find out the meticulous role of activated dendritic cells （DCs） during the human immunodeficiency virus （HIV） infection process. DCs play a dual role by enhancing both HIV infection progression, as well as antiviral immune response. To explore the implications of these dual roles, we have formulated our mathematical model and analyzed the model by both analytical and numerical approaches. By using an impulsive differential equation, we have studied the effect of DC-based vaccination. Analytically we have determined the threshold value of drug dosage and dosing interval for optimum levels of injection. We have also investigated the effect of perfect adherence of drug dose on the immune cell count in extreme cases and observed that, systematic drug dose of the immune cells leads to its maximum level.