scholarly journals Feedback control and its impact on generalist predator–prey system with prey harvesting

2019 ◽  
Vol 24 (5) ◽  
Author(s):  
Debabrata Das ◽  
Tapan Kumar Kar
Keyword(s):  
Feedback Control ◽  
Sustainable Management ◽  
Prey Species ◽  
Fishing Effort ◽  
Maximum Sustainable Yield ◽  
Management Policy ◽  
Generalist Predator ◽  
Predator Density ◽  
Predator Prey ◽  
Prey System

This article examines the effectiveness of feedback control as a management policy on a generalist predator–prey system with prey harvesting. We discuss the result of implementing feedback control with respect to prey and predator separately. This paper also depicts the effect of exploitations up to maximum sustainable yield (MSY). We observe that with a constant fishing effort MSY policy is a sustainable management policy to protect both the species. However, further increase of fishing effort may cause the extinction of prey species. But considering feedback control of fishing effort may restrict the extinction of prey species. When fishing effort is controlled in terms of prey density, the extinction of prey population can be avoided. In this case, there may be coexistences of prey, predator and fishery or extinction of fishery. But when fishing effort is controlled by predator density, it is difficult to manage the coexistences of prey, predator and fishery.  

scholarly journals Comparison and analysis of two forms of harvesting functions in the two-prey and one-predator model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xinxin Liu ◽  
Qingdao Huang
Keyword(s):  
Prey Species ◽  
Equilibrium Points ◽  
Maximum Sustainable Yield ◽  
Predator Prey ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Model ◽  
Model Equations ◽  
The Given

AbstractA new way to study the harvested predator–prey system is presented by analyzing the dynamics of two-prey and one-predator model, in which two teams of prey are interacting with one team of predators and the harvesting functions for two prey species takes different forms. Firstly, we make a brief analysis of the dynamics of the two subsystems which include one predator and one prey, respectively. The positivity and boundedness of the solutions are verified. The existence and stability of seven equilibrium points of the three-species model are further studied. Specifically, the global stability analysis of the coexistence equilibrium point is investigated. The problem of maximum sustainable yield and dynamic optimal yield in finite time is studied. Numerical simulations are performed using MATLAB from four aspects: the role of the carrying capacity of prey, the simulation about the model equations around three biologically significant steady states, simulation for the yield problem of model system, and the comparison between the two forms of harvesting functions. We obtain that the new form of harvesting function is more realistic than the traditional form in the given model, which may be a better reflection of the role of human-made disturbance in the development of the biological system.

PERMANENCE IN A PERIODIC PREDATOR–PREY SYSTEM WITH PREY DISPERSAL AND PREDATOR DENSITY-INDEPENDENT

2006 ◽  
Vol 14 (04) ◽  
pp. 491-507 ◽  
Author(s):  
LONG ZHANG ◽  
ZHIDONG TENG
Keyword(s):  
Periodic Solution ◽  
Prey Species ◽  
Positive Periodic Solution ◽  
Analytic Method ◽  
Predator Density ◽  
Volterra Type ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Theoretical Results

In this paper, we study two-species predator–prey Lotka–Volterra-type dispersal system with periodic coefficients, in which the prey species can disperse among n-patches, but the predator species which is density-independent is confined to some patches and cannot disperse. By utilizing the analytic method, sufficient and realistic conditions on the boundedness, permanence, extinction, and the existence of positive periodic solution are established. The theoretical results are confirmed by a special example and numerical simulations.

Effects of predator–prey interactions and adaptive change on sustainable yield

2004 ◽  
Vol 61 (2) ◽  
pp. 175-184 ◽  
Author(s):  
Hiroyuki Matsuda ◽  
Peter A Abrams
Keyword(s):  
Feedback Control ◽  
Population Size ◽  
Single Species ◽  
Fishing Effort ◽  
Maximum Sustainable Yield ◽  
Adaptive Change ◽  
Sustainable Yield ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Abundance

We explore the effects on population size and yield of different levels of harvesting of a predator in a predator–prey system. We consider the consequences of adaptive change in the predator's foraging time (or effort) and feedback control of fishing effort. The predator may increase in population size with increasing fishing effort, either when the prey is characterized by a positive effect of its own population size on its own growth rate or when the prey is overexploited by the predator. The predator abundance at which the sustainable yield is maximized can be larger than the abundance without fishing. The effort that achieves maximum sustainable yield and the effort that maximizes predator abundance can both be close to the effort at which the stock collapses. Feedback control in the response to predator abundance may fail to achieve the desired abundance of the target stock or its prey even if the fishing effort is well controlled. These results suggest that developing policies for exploiting adaptive predator species in potentially cycling systems cannot be based on the stable single-species models often used in fisheries management.

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.

scholarly journals Permanence for a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jiangbin Chen ◽  
Shengbin Yu
Keyword(s):  
Feedback Control ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Control Variables ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A new set of sufficient conditions for the permanence of a ratio-dependent predator-prey system with Holling type III functional response and feedback controls are obtained. The result shows that feedback control variables have no influence on the persistent property of the system, thus improving and supplementing the main result of Yang (2008).

scholarly journals Permanence of Periodic Predator-Prey System with General Nonlinear Functional Response and Stage Structure for Both Predator and Prey

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Xuming Huang ◽  
Xiangzeng Kong ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Stage Structure ◽  
Functional Responses ◽  
Nonlinear Functional ◽  
Predator Prey ◽  
Prey System

We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.

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