Stability and Optimal Harvesting in a Stage Structure Predator-Prey Switching Strategy

2008 ◽  
pp. 65-80
Author(s):  
Qamar J. A. Khan ◽  
Lakdere Benkherouf ◽  
Nejib Smaoui
Keyword(s):  
Stage Structure ◽  
Optimal Harvesting ◽  
Prey Switching ◽  
Predator Prey ◽  
Switching Strategy

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

scholarly journals Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Can-Yun Huang ◽  
Min Zhao ◽  
Hai-Feng Huo
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Ii Functional Response

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

Bifurcation Analysis and Optimal Harvesting of a Delayed Predator–Prey Model

2015 ◽  
Vol 25 (01) ◽  
pp. 1550012 ◽  
Author(s):  
P. Tchinda Mouofo ◽  
R. Djidjou Demasse ◽  
J. J. Tewa ◽  
M. A. Aziz-Alaoui
Keyword(s):  
Natural Resource Management ◽  
Optimal Control Theory ◽  
Uniform Boundedness ◽  
Optimal Harvesting ◽  
Global Dynamics ◽  
Saddle Node Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Bifurcations ◽  
Prey Model

A delay predator–prey model is formulated with continuous threshold prey harvesting and Holling response function of type III. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The positive invariance of the non-negative orthant is proved and the uniform boundedness of the trajectories. Stability of equilibria is investigated and the existence of some local bifurcations is established: saddle-node bifurcation, Hopf bifurcation. We use optimal control theory to provide the correct approach to natural resource management. Results are also obtained for optimal harvesting. Numerical simulations are given to illustrate the results.

scholarly journals The Dynamic Complexity of a Holling Type-IV Predator-Prey System with Stage Structure and Double Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Yakui Xue ◽  
Xiafeng Duan
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Dynamical Behavior ◽  
Stage Structure ◽  
Point Of View ◽  
Maturation Time ◽  
Dynamic Complexity ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv

We invest a predator-prey model of Holling type-IV functional response with stage structure and double delays due to maturation time for both prey and predator. The dynamical behavior of the system is investigated from the point of view of stability switches aspects. We assume that the immature and mature individuals of each species are divided by a fixed age, and the mature predator only attacks the mature prey. Based on some comparison arguments, sharp threshold conditions which are both necessary and sufficient for the global stability of the equilibrium point of predator extinction are obtained. The most important outcome of this paper is that the variation of predator stage structure can affect the existence of the interior equilibrium point and drive the predator into extinction by changing the maturation (through-stage) time delay. Our linear stability work and numerical results show that if the resource is dynamic, as in nature, there is a window in maturation time delay parameters that generate sustainable oscillatory dynamics.

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