阶段结构远海-近海渔业模型的稳定性及最优收获

§ 1　IntroductionAlong with the development of science and technology,the capacity and output offishing have increased.For example,in China,traditional and backward manual tools areused and the inshore coastlines are limited for fishing,but now gradual improvements inthe technical efficiency of fishing gear and vessels have radically changed the fishing sce-nario.With the advent of sophisticated fishing instruments,the fishing scope has been ex-panded from inshore area to offshore area.As a …     

A ratio‐dependent predator–prey model with stage structure and optimal harvesting policy

In this paper, a ratio‐dependent predator–prey model with stage structure and harvesting is investigated. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence and stability are performed. By constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegative equilibria of the model. The existence possibilities of bioeconomic equilibria have been examined. An optimal harvesting policy is also given by using Pontryagin's maximal principle. Copyright © 2007 John Wiley & Sons, Ltd.     

具有阶段结构和时滞的捕食系统

§ 1　IntroductionThe competitive,cooperative and predator-prey models have been studied by many au-thors.[1— 4] The permanence (or strong persistence) and extinction are significant conceptsof those models.However,the stage structure of species has been considered very little.Inthe real world,almost all animals have the stage structure of immature and mature.Re-cently,papers[5— 7] studied the stage structure of species,the transformation rate of ma-ture population is proportional to the ex…     

Global existence and asymptotic behavior of classical solutions for a 3D two‐species chemotaxis‐Stokes system with competitive kinetics

This paper considers the 2‐species chemotaxis‐Stokes system with competitive kinetics under homogeneous Neumann boundary conditions in a 3‐dimensional bounded domain with smooth boundary. Both chemotaxis‐fluid systems and 2‐species chemotaxis systems with competitive terms were studied by many mathematicians. However, there have not been rich results on coupled 2‐species–fluid systems. Recently, global existence and asymptotic stability in the above problem with (u·∇)u in the fluid equation were established in the 2‐dimensional case. The purpose of this paper is to give results for global existence, boundedness, and stabilization of solutions to the above system in the 3‐dimensional case when is sufficiently small.     

两种群相互竞争的高维SEIR传染病模型全局渐近稳定性

研究了一类两种群相互竞争的非线性高维SEIR传染病数学模型动力学性质,综合利用Lasalle不变集原理,Lyapunov函数,Routh-Hurwitz判据和Krasnoselskii等多种方法,得到了边界平衡点的全局渐近稳定和正平衡点局部渐近稳定的阈值条件.     

GLOBAL ASYMPTOTIC STABILITY OF THE PERIODIC LOTKA-VOLTERRA SYSTEM WITH TWO-PREDATORS AND ONE-PREY

The three species Lotka-Volterra periodic model with two predators and one prey is considered. A set of easily verifiable sufficient conditions is obtained. Finally, an example is given to illustrate the feasibility of these conditious.     

Global asymptotic stability in n-species nonautonomous Lotka–Volterra competitive systems with infinite delays

By means of Lyapunov functional, we have succeeded in establishing the global asymptotic stability of the positive solutions of a delayed n-species nonautonomous Lotka–Volterra type competitive system without dominating instantaneous negative feedbacks. As a corollary, we show that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small.     

ON GLOBAL ASYMPTOTIC STABILITY OF THE ZERO SOLUTION OF A GENERALIZED LIENARD′S SYSTEM

ＯＮＧＬＯＢＡＬＡＳＹＭＰＴＯＴＩＣＳＴＡＢＩＬＩＴＹＯＦＴＨＥＺＥＲＯＳＯＬＵＴＩＯＮＯＦＡＧＥＮＥＲＡＬＩＺＥＤＬＩＥＮＡＲＤ′ＳＳＹＳＴＥＭＰＥＮＧＬＥＱＵＮＡＮＤＨＵＡＮＧＬＩＨＯＮＧＡｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒ，ｗｅｓｔｕｄｙｔ...     

非线性时滞差分议程的全局渐近稳定性

In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained,xn 1=xn xn-1xn-2 a/xmxm-1 xn-2 a,n=0,1…,where a∈(0,∞) and the initial values x-2,x-1,x0∈(0,∞).As a special case,a conjecture by Ladas is confirmed.     

Optimal Harvesting and Stability for a Predator-prey System with Stage Structure

The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.     

Global asymptotic stability of a ratio dependent predator prey system with diffusion and delay

The main concern of this paper is to study the dynamic of a ratio dependent predator-prey system with diffusion and delay. Concretely, we prove that when the system of PDE is persistent the nontrivial equilibrium is globally asymptotically stable. This work was partially supported by CDCHT-ULA. Project SE-C-02-07-05     

Permanence extinction and global asymptotic stability in a stage structured system with distributed delays

In this paper we consider a nonautonomous stage-structured competitive system of n-species population growth with distributed delays which takes into account the delayed feedback in both interspecific and intraspecific interactions. We obtain, by using the method of repeated replace, sufficient conditions for permanence and extinction of the species. The global attractivity of the unique positive equilibrium is proved in the autonomous case. Our results extend previous ones obtained by Liu et al. in [Nonlinear Anal. 51 (2002) 1347-1361; J. Math. Anal Appl. 274 (2002) 667-684].     

具有阶段结构的竞争系统的持久性和稳定性

研究带有时滞和成长阶段的两种群竞争模型,第一个种群分成年和幼年两个阶段,第二个种群不具有阶段结构.本文证明了系统正解的有界性;利用比较原理得到了系统永久生存的充分条件;通过构造Lyapunov函数得到了系统全局渐近稳定的充分条件.     

Global asymptotic stability of CNNs with impulses and multi‐proportional delays

This paper is devoted to global asymptotic stability of cellular neural networks with impulses and multi‐proportional delays. First, by means of the transformation v_i(t) = u_i(e^t), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Second, we prove the global exponential stability of the latter by nonlinear measure, and that the exponential stability of the latter implies the asymptotic stability of the former. We furthermore provide a sufficient condition to the existence, uniqueness, and the global asymptotic stability of the equilibrium point of the former. Our results are generalizations of some existing ones. Finally, an example and its simulation are presented to illustrate effectiveness of our method. Copyright © 2015 John Wiley & Sons, Ltd.     

Global stability of a multistrain SIS model with superinfection and patch structure

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006;7:235–247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters.