oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
Global Stability for a Delayed Predator-Prey System with Stage Structure for the Predator  [PDF]
Xiao Zhang,Rui Xu,Qintao Gan
Discrete Dynamics in Nature and Society , 2009, DOI: 10.1155/2009/285934
Abstract: A delayed predator-prey system with stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of equilibria of the system is discussed. The existence of Hopf bifurcation at the positive equilibrium is established. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and two boundary equilibria of the system. Numerical simulations are carried out to illustrate the theoretical results.
Bifurcation Analysis for a Delayed Predator-Prey System with Stage Structure  [cached]
Jiang Zhichao,Cheng Guangtao
Fixed Point Theory and Applications , 2010,
Abstract: A delayed predator-prey system with stage structure is investigated. The existence and stability of equilibria are obtained. An explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the normal form and the center manifold theory. Finally, a numerical example supporting the theoretical analysis is given.
Periodic solutions of a delayed predator-prey model with stage structure for predator  [PDF]
Rui Xu,M. A. J. Chaplain,F. A. Davidson
Journal of Applied Mathematics , 2004, DOI: 10.1155/s1110757x04308090
Abstract: A periodic time-dependent Lotka-Volterra-type predator-prey model with stage structure for the predator and time delays due to negative feedback and gestation is investigated. Sufficient conditions are derived, respectively, for the existence and global stability of positive periodic solutions to the proposed model.
Singular perturbation method for global stability of ratio-dependent predator-prey models with stage structure for the prey  [cached]
Linfei Nie,Zhidong Teng
Electronic Journal of Differential Equations , 2013,
Abstract: In this article, a singular perturbation is introduced to analyze the global asymptotic stability of positive equilibria of ratio-dependent predator-prey models with stage structure for the prey. We prove theoretical results and show numerically that the proposed approach is feasible and efficient.
Global Existence and Convergence of Solutions to a Cross-Diffusion Cubic Predator-Prey System with Stage Structure for the Prey  [cached]
Cao Huaihuo,Fu Shengmao
Boundary Value Problems , 2010,
Abstract: We study a cubic predator-prey system with stage structure for the prey. This system is a generalization of the two-species Lotka-Volterra predator-prey model. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the global existence of solutions and the stability of equilibrium points to the system of weakly coupled reaction-diffusion type are discussed. Finally, the existence of nonnegative classical global solutions to the system of strongly coupled reaction-diffusion type is investigated when the space dimension is less than 6, and the global asymptotic stability of unique positive equilibrium point of the system is proved by constructing Lyapunov functions.
Global Existence and Convergence of Solutions to a Cross-Diffusion Cubic Predator-Prey System with Stage Structure for the Prey  [cached]
Huaihuo Cao,Shengmao Fu
Boundary Value Problems , 2010, DOI: 10.1155/2010/285961
Abstract: We study a cubic predator-prey system with stage structure for the prey. This system is a generalization of the two-species Lotka-Volterra predator-prey model. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the global existence of solutions and the stability of equilibrium points to the system of weakly coupled reaction-diffusion type are discussed. Finally, the existence of nonnegative classical global solutions to the system of strongly coupled reaction-diffusion type is investigated when the space dimension is less than 6, and the global asymptotic stability of unique positive equilibrium point of the system is proved by constructing Lyapunov functions.
Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey  [PDF]
Zizhen Zhang,Huizhong Yang
Discrete Dynamics in Nature and Society , 2012, DOI: 10.1155/2012/282908
Abstract: This paper is concerned with a Holling type III predator-prey system with stage structure for the prey population and two time delays. The main result is given in terms of local stability and bifurcation. By choosing the time delay as a bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. In particular, explicit formulas that can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form method and center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are also included. 1. Introduction Predator-prey dynamics continues to draw interest from both applied mathematicians and ecologists due to its universal existence and importance. Many kinds of predator-prey models have been studied extensively [1–6]. It is well known that there are many species whose individual members have a life history that takes them through immature stage and mature stage. To analyze the effect of a stage structure for the predator or the prey on the dynamics of a predator-prey system, many scholars have investigated predator-prey systems with stage structure in the last two decades [7–15]. In [7], Wang considered the following predator-prey system with stage structure for the predator and obtained the sufficient conditions for the global stability of a coexistence equilibrium of the system: where represents the density of the prey at time . and represent the densities of the immature predator and the mature predator at time , respectively. For the meanings of all the parameters in system (1.1), one can refer to [7]. Considering the gestation time of the mature predator, Xu [8] incorporated the time delay due to the gestation of the mature predator into system (1.1) and considered the effect of the time delay on the dynamics of system (1.1). There has also been a significant body of work on the predator-prey system with stage structure for the prey. In [12], Xu considered a delayed predator-prey system with a stage structure for the prey: where and denote the population densities of the immature prey and the mature prey at time , respectively. denotes the population density of the predator at time . All the parameters in system (1.2) are assumed positive. is the birth rate of the immature prey. is the transformation rate from immature individual to mature individuals. is the intraspecific competition coefficient of
Stability and bifurcation in a delayed predator-prey system with stage structure and functional response
Xiao Zhang,Rui Xu,Qintao Gan
Electronic Journal of Differential Equations , 2009,
Abstract: In this paper, a delayed predator-prey system with stage structure and Holling type-II functional response is investigated. The local stability of a positive equilibrium and the existence of Hopf bifurcations are established. By using the normal form theory and center manifold reduction, explicit formulae determining the stability, direction of the bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate the theoretical results.
A Stage-Structured Predator-Prey Model with Time Delays
一个具有时滞和阶段结构的捕食-被捕食模型

Xu Rui,Hao Feilong,Chen Lansun,
徐瑞
,郝飞龙,陈兰荪

数学物理学报(A辑) , 2006,
Abstract: A delayed predator-prey model with stage structure for prey is investigated. By constructing suitable Lyapunov functionals, the authors discuss the global attractivity of nonnegative equilibria. A set of easily verifiable sufficient conditions are derived for the permanence and extinction of the proposed ecological system.
Harvesting Control for a Stage-Structured Predator-Prey Model with Ivlev's Functional Response and Impulsive Stocking on Prey  [PDF]
Kaiyuan Liu,Lansun Chen
Discrete Dynamics in Nature and Society , 2007, DOI: 10.1155/2007/86482
Abstract: We investigate a delayed stage-structured Ivlev's functional response predator-prey model with impulsive stocking on prey and continuous harvesting on predator. Sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system are obtained. These results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for the biological resource management and enrich the theory of impulsive delay differential equations.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.