Positive periodic solutions of nonautonomous delay competitive systems with weak Allee effect

This paper considers a nonautonomous Lotka–Volterra type multispecies competitive system with weak Allee effect and delays. The model has the intraspecific competition terms defined by sign changing functions which depend on population density monotonically and time periodically. An existence theorem of positive periodic solutions is established using the coincidence degree theory. Furthermore, for the case of constant delays, a sufficient condition for the positive periodic solution to be globally attractive is proved with the Lyapunov method so that the system attains permanence.     

二次微分系统的反射函数及其周期解

本文给出了二镒多项式微分系统具有满足特定关系式的反射函数和存在周期解的充要条件，以及在此条件下反射函数的具体表达式及周期解的稳定性态。     

具有Holling功能反应的非自治捕食系统的持续性和周期解

研究了具有一般的Holling功能反应函数,且种群之间既有捕食关系,又有竞争关系的三种群混合模型,得到了该系统惟一存在全局渐近稳定正周期解的条件,推广了已有结论.     

Asymptotic behavior of solutions of a periodic diffusion system of plankton allelopathy

This paper is concerned with the existence and asymptotic behavior of periodic solutions for a periodic reaction diffusion system of a planktonic competition model under Dirichlet boundary conditions. The approach to the problem is by the method of upper and lower solutions and the bootstrap argument of Ahmad and Lazer. It is shown under certain conditions that this system has positive or semi-positive periodic solutions. A sufficient condition is obtained to ensure the stability and global attractivity of positive periodic solutions.     

一类非线性微分系统的反射函数与周期解

采用一种新方法-反射函数法给出了一类非线性微分系统具有满足特定关系式的反射函数和存在周期解的充要条件,得到了此条件下反射函数的具体表达式和周期解的稳定性态.     

具有阶段结构且食饵有避难所的模型分析

研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件.     

具有离散时滞的非自治扩散模型的周期解

考虑具有离散时滞及周期系数的非自治的两种群竞争扩散摸型,利用微分不等式等获得了其一致持续生存的条件,通过构造李亚普诺夫泛函获得了其正周期解存在与全局渐近稳定的充分条件.     

具有连续时滞的非自治扩散Lotka-volterra模型的渐近性

持续生存概念是种群生态系统稳定性的一个重要描述,而研究竞争种群共存的问题是种群生态学的一个重要问题,考虑非自治的两种群L otka-vo lterra周期系数的时滞扩散摸型,通过构造李亚普诺夫泛函,微分不等式等获得了其一致持续生存及正周期解存在与全局渐近稳定的充分条件.     

Stability and Hopf bifurcation of a modified delay predator-prey model with stage structure

In this paper, a modified delay predator-prey model with stage structure is established, which involves the economic factor and internal competition of all the prey and predator populations. By the methods of normal form and characteristic equation, we obtain the stability of the positive equilibrium point and the sufficient condition of the existence of Hopf bifurcation. We analyze the influence of the time delay on the equation and show the occurrence of Hopf bifurcation periodic solution. The simulation gives a visual understanding for the existence and direction of Hopf bifurcation of the model.     

具有时滞的三个混合种群模型的周期解

利用重合度理论中连续性定理 ,得到了三种群时滞混合模型正周期解存在性的判别准则     

Global stability and pattern formation in a nonlocal diffusive Lotka–Volterra competition model

A diffusive Lotka–Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka–Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper–lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients.     

Positive periodic solutions for Lotka–Volterra systems with a general attack rate

The paper deals with a non-autonomous Lotka–Volterra type system, which in particular may include logistic growth of the prey population and hunting cooperation between predators. We focus on the existence of positive periodic solutions by using an operator approach based on the Krasnosel’skii homotopy expansion theorem. We give sufficient conditions in order that the localized periodic solution does not reduce to a steady state. Particularly, two typical expressions for the functional response of predators are discussed.     

Analysis of dynamics in a general intraguild predation model with intraspecific competition

This paper is devoted to studying the dynamical properties of a general intraguild predation model with intraspecific competition. We first investigate the stability of all possible equilibria in relation to the ecological parameters, and then study the long time behavior of the solution. Moreover, we provide a detailed analysis of dynamics of a IGP model with linear functional response and intraspecific competition. Our results show that the impact of the intraspecific competition essentially increases the dynamical complexity of the system.     

Persistence and Periodic Solution on a Nonautonomous SIS Model with Delays

An SIS model with periodic maximum infectious force,recruitment rate and removal rate of the infectives has been investigated in this articale.Sufficient conditions for the permanence and extinction of the disease are obtained.Furthermore,The existence and global stability of positive periodic solution are established.Finally,we present a procedure by which one can control the parameters of the model to kccp the infcctivcs stay eventually in a desired set.     

Persistence and stability in general nonautonomous single-species Kolmogorov systems with delays

This paper studies the general nonautonomous single-species Kolmogorov systems with delays. The sufficient conditions on the persistence and permanence of species, global asymptotic stability and the existence of positive periodic solutions are established. As applications of these results, the permanence, global asymptotic stability and the existence of positive periodic solutions for a series of special single-species growth systems with delays are discussed.     

Hopf bifurcation analysis in a multiple delayed innovation diffusion model with Holling II functional response

A nonlinear mathematical model with Holling II functional response describing the dynamics of nonadopter and adopters population in a stage structured innovation diffusion model, which incorporates the evaluation stage (multiple delays), is proposed. Firstly, we study the stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays at the positive equilibrium by analyzing the distribution of the roots of the corresponding exponential characteristic equation obtained through the variational matrix. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined with the help of normal form theory and center manifold theorem. Meanwhile, various cases are discussed to examine the effect of different delays on the stability of delayed innovation diffusion system and are also established numerically. It is also observed that the cumulative density of external influences has a significant role in developing maturity stage (adoption stage) in the system. Finally, numerical simulations are carried out to support and supplement the analytical findings.     

Globally asymptotical stability and periodicity for a nonautonomous two-species system with diffusion and impulses

Existence and globally asymptotical stability of positive periodic solutions for a nonautonomous two-species competition system with diffusion and impulses are studied in this paper. By employing Mawhin continuation theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one positive periodic solution, and by means of a suitable Lyapunov functional, the globally asymptotical stability of positive periodic solution is presented. Finally, an illustrative example and simulations are given to show the effectiveness of the main results.     

非自治的具有阶段结构和时滞的捕食系统的动力学行为

本文研究了一个非自治的具有阶段结构和时滞的捕食-食饵模型.利用比较原理获得了系统持久性的条件,在假设系统为周期系统的条件下通过构造Liapunov函数证明了正周期解的存在唯一性和全局渐近稳定性.     

Periodic solutions of a nonautonomous predator–prey system with stage structure and time delays

A nonautonomous Lotka–Volterra type predator–prey model with stage structure and time delays is investigated. It is assumed in the model that the individuals in each species may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not feed on prey and do not have the ability to reproduce. By some comparison arguments we first discuss the permanence of the model. By using the continuation theorem of coincidence degree theory, sufficient conditions are derived for the existence of positive periodic solutions to the model. By means of a suitable Lyapunov functional, sufficient conditions are obtained for the uniqueness and global stability of the positive periodic solutions to the model.     

非自治Kolmogorov竞争系统的严格正解

In this paper, the existence of strictly positive solutions for N species normutonomous Kolmogorov competition systems is studied. By applying the Schauder‘s flxed pointtheorem some new sufficient conditions are established. In particular, for the almost periodicsystem, tile existence of strictly positive almost periodic solutiorts is obtained, Some previousresults are improved and generalized.