scholarly journals Periodic solutions of a delayed predator-prey model with stage structure for predator

2004 ◽  
Vol 2004 (3) ◽  
pp. 255-270 ◽  
Author(s):  
Rui Xu ◽  
M. A. J. Chaplain ◽  
F. A. Davidson
Keyword(s):  
Periodic Solutions ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Time Dependent ◽  
Volterra Type ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Proposed Model

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.

scholarly journals Existence and Uniqueness of Positive Periodic Solutions for a Delayed Predator-Prey Model with Dispersion and Impulses

2014 ◽  
Vol 2014 ◽  
pp. 1-21
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Liu Yang ◽  
Zhenghui Gao ◽  
Yunhui Zeng
Keyword(s):  
Periodic Solutions ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Predator Population ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

An impulsive Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments and time delays is investigated, where we assume the model of patches with a barrier only as far as the prey population is concerned, whereas the predator population has no barriers between patches. By applying the continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness, and global stability of positive periodic solutions of the system. Some known results subject to the underlying systems without impulses are improved and generalized. As an application, we also give two examples to illustrate the feasibility of our main results.

scholarly journals Global Property in a Delayed Periodic Predator-Prey Model with Stage-Structure in Prey and Density-Independence in Predator

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaolin Fan ◽  
Zhidong Teng ◽  
Haijun Jiang
Keyword(s):  
Sufficient Conditions ◽  
Stage Structure ◽  
Global Property ◽  
Predator Density ◽  
Predator Prey ◽  
Density Independence ◽  
Predator Prey Model ◽  
Prey Model ◽  
Density Dependency ◽  
Integrable Form

We study the global property in a delayed periodic predator-prey model with stage-structure in prey and density-independence in predator. The sufficient conditions on the ultimate boundedness of all positive solutions are obtained, and the sufficient conditions of the integrable form for the permanence and extinction are further established, respectively. Some well-known results on the predator density-dependency are improved and extended to the predator density-independent cases. The theoretical results are confirmed by the special examples and the numerical simulations.

EXISTENCE OF PERIODIC SOLUTIONS OF NONAUTONOMOUS PREDATOR-PREY MODEL WITH BEDDINGTON-DEANGELIS FUNCTIONAL RESPONSE AND TIME DELAY

2021 ◽  
Vol 10 (5) ◽  
pp. 2641-2652
Author(s):  
S. Mahalakshmi ◽  
V. Piramanantham
Keyword(s):  
Time Delay ◽  
Periodic Solutions ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Existence Of Periodic Solutions

In this paper we establish some easily verifiable sufficient conditions for the existence of periodic solutions of nonautonomous Predator-Prey Model with Beddington-DeAngelis Functional response and time delay using Mowhins Coincidence degree method.

scholarly journals Positive Periodic Solutions of a Neutral Impulsive Predator-Prey Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Guirong Liu ◽  
Xiaojuan Song
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Impulsive System ◽  
Impulsive Effect ◽  
Neutral System ◽  
Positive Periodic Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

We investigate a ratio-dependent predator-prey model with Holling type III functional response based on system of neutral impulsive differential equations. Sufficient conditions for existence of positive periodic solutions are obtained by applying continuation theorem. Our main results demonstrate that under the suitable periodic impulse perturbations, the neutral impulsive system preserves the periodicity of the corresponding neutral system without impulse. In addition, our results can be applied to the corresponding system without impulsive effect, and thus, extend previous results.

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