Global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion

By employing the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion is established. Further, by constructing a Lyapunov functional and using the result of the existence of positive periodic solution, the attractivity of a positive periodic solution for above system is obtained.     

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．     

一类具有时滞功能反应的两种群捕食-食饵脉冲扩散系统的周期解

本文研究了一类具有脉冲的时滞功能反应的两种群捕食-食饵扩散模型的周期解存在性问题.应用重合度理论方法和不等式的分析理论,得到该系统正周期解存在的充分条件.     

一个周期中立型对数种群模型

本文获得了周期中立型对数种群模型N(t)=N(t)(r(t)-α(t)log[N(t-σ)]-b(t)d/dtlog[N(t-r)])的周期正解的存在性及对所有正解的吸引性．     

含参数泛函微分方程概周期正解的存在性

研究了一类含参数泛函微分方程概周期正解的存在性问题.结合有界性及渐近概周期性获得了系统存在概周期正解的几组充分条件,并将结果应用于几类种群动力学模型,分别获得了系统在概周期环境下存在概周期解的一组充分条件.     

POSITIVE PERIODIC SOLUTION TO A CLASS OF NONLINEAR PERIODIC DIFFERENTIAL EQUATION WITH IMPULSES AND DELAY

In this paper, by using a fixed point theorem of Krasnoselskii, we study the positive periodic solution for a class of nonlinear periodic differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results of the existence of positive periodic solution about the equation are obtained.     

Positive periodic solution for a neutral delay competitive system

In this paper we study the existence of positive periodic solutions for a class of neutral type competitive system with delay. Applying the continuation theorem of coincidence degree theory, a general criteria on the existence of positive periodic solutions are established. Some the related results are generalized and improved. It is shown that the arguments delays have no effect on the existence positive periodic solution of system.     

一类Chemostat捕食模型正周期解的存在性

讨论了一类Chemostat捕食模型在一定条件下正周期解的存在性问题.运用周期抛物型算子理论、Schauder估计和分歧理论得到了该模型正周期解存在的充分必要条件.     

Existence and global attractivity of positive periodic solutions for impulsive predator–prey model with dispersion and time delays

In this paper, we study the existence and global attractivity of positive periodic solutions for impulsive predator–prey systems with dispersion and time delays. By using the method of coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solution, and by means of a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are presented. Some known results subject to the underlying systems without impulses are improved and generalized.     

一类具无穷时滞 Nicholson’s blowflies模型的正概周期解(英文)

通过利用锥上的不动点定理,本文主要研究具无穷时滞Nicholson’s blowflies模型的正概周期解的存在唯一性.从而得到此正概周期解存在唯一性和指数收敛的充分条件.最后给出一个例子说明本文结果的可行性.     

PERIODIC SOLUTION AND ALMOST PERIODIC SOLUTION OF NONAUTONOMOUS COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTING

In this paper, a two-species nonautonomous competitive model with stage structure and harvesting is considered. Sufficient conditions for the existence, uniqueness, global attractivity of positive periodic solution and the existence, uniform asymptotic stability of almost 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.     

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．     

关于一个多滞量周期Logistic方程

证明了方程的周期正解的存在性,并获得了该周期正解为全局吸引的充分条件。     

Periodic solution of a two-species competitive system with toxicant and birth pulse

In this paper, we study the existence of positive periodic solution of two-species competitive system with toxicant and birth pulse. A set of easily verifiable sufficient conditions are derived for the existence of at least one positive periodic solution of the above system by using the method of coincidence degree. Numerical simulations are also presented to illustrate the feasibility of our main results.     

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.     

Dynamic analysis of a turbidostat model with the feedback control

In this paper, a mathematical model with impulsive state feedback control is proposed for turbidostat system. The sufficient conditions of existence of positive order one periodic solution are obtained by using the existence criteria of periodic solution of a general planar impulsive autonomous system. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate and the initial concentration of microorganism and substrate. By investigating the periodic solution, the period and the initial point of the periodic solution are given. The results show that turbidostat with impulsive state feedback control tends to an order one periodic solution.     

Positive periodic solution of two-species ratio-dependent predator–prey system with time delay in two-patch environment

In this paper, we are concerned with the existence of positive periodic solution to a class of two-species ratio-dependent predator–prey diffusion model with time delay. By using the continuation theorem of coincidence degree theory, we transform this problem into a problem of calculating the topological degree of a continuous mapping, and then some sufficient conditions of the existence of positive periodic solution is established for the system.     

A periodic predator–prey-chain system with impulsive perturbation

A periodic predator–prey-chain system with impulsive effects is considered. By using the global results of Rabinowitz and standard techniques of bifurcation theory, the existence of its trivial, semi-trivial and nontrivial positive periodic solutions is obtained. It is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi-trivial periodic solution. Furthermore, the stability of these periodic solutions is studied.     

Dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate

In this paper, the dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate are analyzed. The existence and uniqueness of the global positive solution is proved by constructing the equivalent system without pulses. The threshold which determines the extinction and persistence of the disease is obtained. The global attraction of disease-free periodic solution is addressed. Sufficient condition for the existence of a positive periodic solution is established. These results are supported by computer simulations.