中立型单种群模型周期正解存在性问题

利用抽象连续的k 集压缩原理研究一类中立型单种群模型[SX(]dN[]dt[SX)]=N(t)［a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))］ 周期正解的存在性问题,得到了周期正解存在性的若干结论,改进和推广了已有的工作     

N（t）=N（t）[a（t）-∑n i=1bi（t）Ni（t-τi（t））]的周期正解

用非线性分析的方法讨论了方程N（t）=N（t）[a（t）-∑n i=1bi(t)Ni(t-τi（t）)]的周期正解的存在性，所获结果包含或推广了已有的几上结论[2，3]。     

关于中立型时滞模型的周期正解

本文利用拓扑度理论和某些新技巧,研究了一类中立型时滞模型N′(t)=N(t)［a(t)-b(t)N(t-τ(t))-c(t)N′(t-τ(t))］周期正解的存在性,得到了一些新结果,解决了一个公开问题,并推广、改进了一些已知文献的结果,同时也改正了文［3］中微分运算的错误和定理2.     

一类非线性连续分布时滞系统的周期正解

研究一类非线性周期连续时滞传染病模型ny′i(t)=-αi(t)yi(t)+(ci(t)-yi(t))∑j=1βij(t∫)0-TKj(s)yj(t+s)ds,i=1,2,…,n作者主要讨论了该传染病模型的周期正解的全局存在性,运用重合度延拓理论证明了该模型至少存在一个满足容许值的ω-周期正解.     

二阶周期边值问题的多重正解

考虑如下周期边值问题:其中x~([1])(t)=p(t)x'(t).总假设p(t)>0,q(t)>0,且f(t,x)是[0,1]×(0,+∞)→[0,+∞)的连续函数,f在z=0可以有奇性.利用锥不动点定理以及格林函数的正性,给出周期边值问题单个和多个正解存在性证明的一种新方法.在实际中,定理的条件很容易验证.     

中立型对数种群模型正周期解的存在性新结果

运用k-集压缩算子的拓扑度抽象连续定理,研究了如下一类高阶微分方程的周期解存在性问题x(m)(t)= r(t)-a(t)x(t-σ)-b(t)x(m)(t-τ).并将其应用于研究一类中立型对数种群模型dN/dt= N(t) [r(t)-a(t) In N(t-σ-b(t)d/(dt)In N(t-τ)]的正周期解存在性...     

有序Banach空间中非线性二阶周期边值问题的正解

讨论了有序Banach空间E中的非线性二阶周期边值问题-u″(t)+bu′(t)+cu(t)=f(t,u(t)),0≤t ≤ ω,u(0)=u(ω),u′(0)=u′(ω)正解的存在性,其中b,c∈R且c＞0,f:[0,ω]×P→P连续,P为E中的正元锥.本文通过新的非紧性测度的估计技巧与凝聚映射的不动点指数理论,获得了该问题正解的存在性结果.     

Lienard方程的周期解

主要利用Leray-Schauder不动点理论研究Lienard方程周期边值问题x f(x)x g(t,x)=e(t)x(0)=x(T),x(0)=x(T)的正解及多个正解的存在性.     

非线性中立型时滞方程解的全局渐近稳定性和振动性

本文研究非线性中立型时滞微分方程N( t) =N( t) [a( t) -b( t) N ( t-τ) -c( t) N( t-σ) -d( t) N ( t) ],t≥ t0 ,( E)其中τ,σ∈ [0 ,∞ ) ,a( t) ,b( t) ,d( t)∈ C1( [t0 ,∞ ) ,R+) ,c( t)∈ C( [t0 ,∞ ) ,k) ,得到方程 ( E)的正解关于正常数平衡点全局渐近稳定和振动的充分条件 .本文所用方法与其他文献不同 ,所得结果发展了一些文献的结果 ,其中定理 ( 2 .3)回答了由 Y.Kuang and A.Feldstein所提出的一个公开问题 .     

脉冲中立型时滞微分方程的正解的存在性

本文证明了线性脉冲中立型微分方程 [y(t)+p(t)y(t-τ)-r(t)y(t-ρ)]′+q(t)y(t-σ)=0,t≥0,t≠t_k, y(t_k~+)-y(t_k)=b_ky(t_k),k=1,2,…正解的存在性等价于一类非脉冲中立型方程正解的存在性,应用这一结果,建立了此类线性脉冲中立型微分方程正解存在性的若干充分条件。     

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. Some sufficient conditions for oscillation of all positive solutions about the positive periodic solution are established and also some sufficient conditions for the global attractivity of the periodic solution are obtained.     

GLOBAL ATTRACTIVITY IN A PERIODIC DELAY SINGLE SPECIES MODEL

In this paper, we establish the existence of a positive periodic solution for a periodic delay single species population growth model, and obtain sufficient conditions for the periodic solution to be globally attractive.     

Dynamic behavior of an eco-epidemic system with impulsive birth

In the paper, we investigate an eco-epidemic system with impulsive birth. The conditions for the stability of infection-free periodic solution are given by applying Floquet theory of linear periodic impulsive equation. And we give the conditions of persistence by constructing a consequence of some abstract monotone iterative schemes. By using the method of coincidence degree, a set of sufficient conditions are derived for the existence of at least one strictly positive periodic solution. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels.     

Periodicity and stability for a Lotka-Volterra type competition system with feedback controls and deviating arguments

This paper deals with the general periodic Lotka-Volterra type competition systems with feedback controls and deviating arguments. By employing fixed point index theory on cone, an explicit necessary and sufficient condition for the global existence of the positive periodic solution of the systems is proved. By constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions for the global asymptotic stability of the positive periodic solution of the systems is given.     

Dynamics of a class of non-autonomous systems of two non-interacting preys with common predator

In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution.     

POSITIVE PERIODIC SOLUTION OF A PREDATOR-PREY SYSTEM WITH TIME DELAY

By using continuation theorem in coincidence degree theory,we study the existence of positive periodic solution for a delay and mutual interference predator- prey system with functional response,and obtain sufficient conditions for the existence of positive periodic solution.     

周期时滞Logistic方程的全局吸引性

该文建立了周期时滞Logistic方程N'（t）=r（t）N（t）[1-N（t-τ）／k（t）]的正周期解的存在性，并获得了正周期解的唯一性和全局吸引性的充分条件．所得结果推广和改进了[1]的结果．     

中立型Lotka-Volterra系统正周期解的存在性

利用迭合度理论的连续定理，讨论了一类中立型系统的正周期解的存在性．得到了正周期解存在的一些充分条件．     

时标上具Allee效应的动力学方程的概周期解

本文研究了时标上具Allee效应的可再生资源动力学方程的概周期解的存在性与稳定性.利用线性系统指数二分性与压缩映射不动点定理,得到了方程存在唯一概周期解的充分条件.此外,通过构建适当的Laypunov函数,得到了概周期解是全局指数稳定的充分条件.     

Positive almost periodic solution for a class of Lasota-Wazewska model with infinite delays

By utilizing a fixed theorem in cones, we study the existence of a unique positive almost periodic solution for a generalized Lasota-Wazewska model with infinite delays. Some sufficient conditions which ensure the existence of a unique positive almost periodic solution are derived and it cannot be obtained by the contraction mapping principle. Furthermore, under proper conditions, we establish some criteria to ensure that all solutions of this model converge exponentially to a positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result.