Existence of periodic solutions to a system with functional response on time scales

This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.     

Existence of periodic solutions for a predator-prey system with sparse effect and functional response on time scales

In this paper, we systematically investigates the existence of periodic solutions of a predator-prey system with sparse effect and Beddington-DeAngelis or Holling III functional response on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the systems. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.     

具有比率型功能反应的时标动力学系统的周期解

研究了一类具有比率型功能反应的食物链时标动力学系统,利用重合度理论中的延拓定理讨论了此系统周期解的存在性问题,得到了保证周期解存在的充分条件,从而使这一类系统的连续与离散情形:微分方程和差分方程的周期解存在性问题得到了统一研究.     

时标上一类非自治捕食系统的周期解(英文)

本文在时标上运用迭合度理论中的Gaines和Mawhin连续性定理研究了一类非自治捕食系统的周期解的存在性,得到了此模型周期解存在的充分条件,该方法可将证明连续和离散微分方程的周期解的存在性统一起来.     

时间测度上具有时滞基于半比率的捕食者-食饵扩散系统的周期解

在时间测度上研究一类具有时滞和基于半比率且有功能性反应的两种群捕食者-食饵扩散系统,利用Mawhin重合度理论建立了这类系统的周期解存在的一个充分性判据.从而使这一类系统的连续与离散情形即相应的微分方程和差分方程的周期解存在性问题得到了统一研究.     

时标上具有阶段结构的三种群捕食系统的周期解

研究了时标上具有阶段结构的三种群捕食系统.运用时标上连续拓扑度定理,得到了系统存在周期解的充分条件.其研究方法使系统的连续时间情形和离散时间情形的周期解问题得到了统一,被广泛地应用来研究微分方程和差分方程的周期解的存在问题.     

时间测度上具有Holling-N类功能反应和扩散的捕食系统的周期解

在时间测度上研究了一类具有Holling-N类功能反应和扩散的捕食系统,利用Mawhin重合度理论建立了这类系统周期解存在的一些新的充分性判据,从而使这一类系统的连续与离散情形,即相应的微分方程和差分方程的周期解存在性问题得到了统一.     

带有Leslie-Gower功能性反应的三维食物链模型研究

研究了离散时间上带有Leslie-Gower功能性反应的三维食物链模型.首先给出保证系统永久持续生成的条件,由于系统系数的周期性,正周期解是存在的,最后通过在正的周期解领域内线性化系统,并通过构造Lyapunov函数,我们得出了保证系统正周期解全局稳定的条件.     

Multiple positive periodic solutions of a delayed discrete predator–prey system with type IV functional responses

In this paper, a discrete periodic predator–prey system with type IV functional responses and time delay is investigated. Using Gaines and Mawhin’s continuation theorem from coincidence degree theory as well as some prior estimates, we get sufficient conditions for the existence of positive periodic solutions of the system. This is also the first time that the coincidence degree theory has been used to obtain multiple positive periodic solutions in discrete ecological systems.     

Does a population with the highest turnover coefficient win competition?

We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We compare dynamical properties of this model with its continuous counterpart. We give sufficient conditions for competitive exclusion and the existence of periodic solutions related to the classical logistic, Beverton–Holt and Ricker models.     

Positive periodic solution for ratio-dependent <Emphasis Type="Italic">n</Emphasis>-species discrete time system

In this paper, sharp a priori estimate of the periodic solutions is obtained for the discrete analogue of the continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modelling the dynamics of the n−1 competing preys and one predator having nonoverlapping generations. Based on more precise a priori estimate and the continuation theorem of the coincidence degree, an easily verifiable sufficient criterion of the existence of positive periodic solutions is established. The result obtained in this paper greatly improves the existing results.     

一类带反馈控制的非自治离散竞争系统概周期解的动力学性质

本文利用差分方程的比较原理以及构造国合适的Lyapunov函数,讨论了一类带有反馈控制的非自治离散竞争系统的持久性和概周期解,给出了存在正概周期解的几个充分条件.最后给出一个数值例子验证了本文主要结果的有效性.     

Almost automorphic solutions to logistic equations with discrete and continuous delay

We obtain sufficient conditions for the existence and uniqueness of a positive compact almost automorphic solution to a logistic equation with discrete and continuous delay. Moreover, we provide a counterexample to some results in literature which deal with the uniqueness of almost periodic solutions to logistic type equations.     

EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A DELAYED PERIODIC PREDATOR-PREY MODEL OF IVLEV TYPE

A periodic coefficients predator-prey system of Ivlev type with both discrete and continuous time delay is investigated. A sufficient condition of the existence of positive periodic solution is established for the system by using the continuation theorem of coincidence degree theory.     

Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system

With the help of differential equations with piecewise constant arguments, we first propose a discrete analogue of continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modeling the dynamics of the prey and the predator having nonoverlapping generations. Then, easily verifiable sufficient criteria are established for the existence of positive periodic solutions. The approach is based on the coincidence degree and the related continuation theorem as well as some priori estimates.     

带扩散项捕食差分系统的周期解

本文给出了带扩散项捕食系统的离散模拟 ,利用一致拓扑度理论获得了离散模型正概周期解的存在性结论 ,改进了一些条件 .这体现了我们采用的离散模拟继承了连续系统的一些动力学性质     

Periodic Solutions of Nonautonomous Discrete Predator-Prey System of Lotka-Volterra Type

A sufficiency criterion is established for the existence of positive periodic solutions of a nonautonomous discrete time predator-prey system of Lotka-Volterra type. Our approach is based on the coincidence degree and the related continuation theorem as well as some priori estimates.     

Multibump solutions for discrete periodic nonlinear Schrödinger equations

In this paper, we study the existence of multibump solutions for discrete nonlinear Schrödinger equations with periodic potentials. We first reduce the existence of multibump homoclinic solutions to the existence of an isolated homoclinic solution with a nontrivial critical group. Then, we study the existence of homoclinics with nontrivial critical groups for both superlinear and asymptotically linear discrete periodic nonlinear Schrödinger equations, and we provide simple sufficient conditions for the existence of homoclinics with nontrivial critical groups in the positive definite case. As an application, we get, without any symmetry assumptions, infinitely many geometrically distinct homoclinic solutions with exponential decay at infinity.     

Existence regions of positive periodic solutions for a discrete hematopoiesis model with unimodal production functions

A discrete model describing the increase and decrease of blood cells is considered in this paper. This hematopoiesis model is a discretization of a delay differential equation with unimodal production function whose coefficients and delays are periodic discrete functions with ω-period. This paper is concerned with the existence of positive ω-periodic solutions. Our results are proved by using the well-known continuation theorem of coincidence degree theory. The existence range of the positive ω-periodic solutions is also clarified. A concrete example and its simulation are also given to illustrate our result. Finally, we examine how positive numbers and coefficients making up our model influence the upper and lower limits of blood cell counts.