scholarly journals Dynamics of Intra-guild Predation Model with Stage Structure in Prey

2021 ◽  
Vol 18 (1) ◽  
pp. 67-77
Author(s):  
Hukmah Hukmah ◽  
Syamsuddin Toaha ◽  
Jeffry Kusuma
Keyword(s):  
Equilibrium Point ◽  
Stage Structure ◽  
Type I ◽  
Functional Responses ◽  
Numerical Result

The Intra-guild predation model is an interaction between three species where two of them compete and prey on each other for the same resource. This study considers the stage structure of prey on and combines Beddington-DeAngelis and Holling type I as functional responses in the model. Furthermore, the equilibrium point and stability of the model will be analyzed. The numerical result at the equilibrium point shows that the solution converging toward the equilibrium point so that the population is stable and will not become extinct with increasing time. In addition, the population tends to be stable when the density of prey is larger than the predator.

scholarly journals A Novel Prey-Predator Quadratic Harvesting Model via Optimal Control Theory and Hopf Bifurcation

2020 ◽  
Vol 1 ◽  
pp. 1-22
Author(s):  
Prabir Panja ◽  
Dipak Kumar Jana
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Fish Species ◽  
Interaction Model ◽  
Existence Condition ◽  
Optimal Harvesting ◽  
Selling Price ◽  
Type I ◽  
Functional Responses ◽  
Proposed Model

In this investigation, a predator-prey interaction model among Phytoplankton, Zooplankton and Fish has been developed. In the absence of Zooplankton and Fish, it is assumed that Phytoplankton grows logistically. It is assumed that Zooplankton consumes Phytoplankton and Fish consumes Phytoplankton as well as Zooplankton. Holling type I & II functional responses have been considered to formulate the our proposed model. It is considered that Phytoplankton releases some toxin in the aquatic environment which makes some death in Zooplankton population. Quadratic harvesting is considered on Fish species. Boundedness of the solution of our proposed model has also been studied. Local stability of the system around each equilibrium point has been investigated. Also, the global stability of the interior equilibrium point has been studied. Existence condition of Hopf bifurcation of our proposed system has been studied. It is found that half saturation constant (α) can change the system dynamics. It is also found that the harvesting rate of Fish (E) and consumption rate of Zooplankton (γ1) has a significant role in the stability of the system. Again, it is found that the harvesting of Fish species will be increased if the selling price of Fish (p) and the annual discount (δ1) of Fish production cost increases. It is also found that the optimal harvesting rate of Fish decreases due to the increase of cost (c) of harvesting of Fish. Finally, some numerical simulation results have been presented to verify our analytical findings.

scholarly journals Dinamika Model Predator Hama Wereng Batang Cokelat (Nilaparvata Lugens) Pada Tanaman Padi Dengan Penerapan Pestisida

Faktor Exacta ◽  
2018 ◽  
Vol 11 (1) ◽  
pp. 94
Author(s):  
Iim Abdul Karim
Keyword(s):  
Equilibrium Point ◽  
Nilaparvata Lugens ◽  
Logistic Function ◽  
Type I ◽  
Font Size ◽  
Functional Responses ◽  
Existence And Stability ◽  
Predator Model ◽  
Two Parameters ◽  
The Mathematical Model

<p><span><span lang="IN"><span style="font-size: medium;">Abstract. In this paper, the mathematical model we discuss the interactions among pests, predators, and effect of pesticides. Interactions between predators and pests use functional responses of Holling type I and type II and the growth of susceptible pests classes satisfied the logistic function. By this model, the existence and stability of the equilibrium point were performed. The existence of the equilibrium point, and were obtained which depend on the threshold parameter, while the equilibrium point did not depend on the parameter. The analysis of equilibrium point stability by this model discussed only on the local stability. To facilitate interpretation of the dynamics between predators, pests and the effects of pesticides, numerical simulations perform indicated by the changes in two parameters bifurcation analysis.</span></span></span></p><p><span><span lang="IN"><span style="font-size: medium;"> </span></span></span><span><span lang="IN">Keywords: Pest predator model, <span>stability,</span> numerical simulation, bifurcation</span></span></p>

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 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.

scholarly journals A Stage-Structure Rosenzweig-MacArthur Model with Effect of Prey Refuge

2020 ◽  
Vol 1 (1) ◽  
pp. 1-7
Author(s):  
Lazarus Kalvein Beay ◽  
Maryone Saija
Keyword(s):  
Equilibrium Point ◽  
Local Stability ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Structure Population ◽  
Prey Refuge ◽  
Behavioral System ◽  
Trivial Equilibrium ◽  
Coexistence Equilibrium

We proposed and analyzed a stage-structure Rosenzweig-MacArthur model incorporating a prey refuge.  It is assumed that the prey is a stage-structure population consisting of two compartments known as immature prey and mature prey. The model incorporates the functional response Holling type-II. In this work, we investigate all the biologically feasible equilibrium points, and it is shown that the system has three equilibrium points. Sufficient conditions for the local stability of the non-negative equilibrium point of the model are also derived. All points are conditionally locally asymptotically stable. By constructing Jacobian matrix and determined eigenvalues, we analyzed the local stability of the trivial equilibrium and non-predator equilibrium points. Specifically for coexistence equilibrium point, Routh-Hurwitz criterion used to analyze local stability. In addtion, we investigated the effect of immature prey refuge. Our mathematical analysis exhibits that immature prey refuge have played a crucial role in the behavioral system. When the effect of immature prey refuge (constant m) increases, it is can stabilize non-predator equilibrium point, where all the species can not exists together. And conversely, if contant m decreases, it is can stabilize coexistence equilibrium point then all the species can exists together. The work is completed with a numerical simulation to confirmed analitical results

An impulsive two-stage predator–prey model with stage-structure and square root functional responses

2016 ◽  
Vol 119 ◽  
pp. 91-107 ◽  
Author(s):  
Xiangmin Ma ◽  
Yuanfu Shao ◽  
Zhen Wang ◽  
Mengzhuo Luo ◽  
Xianjia Fang ◽  
...  
Keyword(s):  
Stage Structure ◽  
Square Root ◽  
Functional Responses ◽  
Two Stage ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Consumer-food systems: why type I functional responses are exclusive to filter feeders

2004 ◽  
Vol 79 (2) ◽  
pp. 337-349 ◽  
Author(s):  
Jonathan M. Jeschke ◽  
Michael Kopp ◽  
Ralph Tollrian
Keyword(s):  
Food Systems ◽  
Type I ◽  
Functional Responses ◽  
Filter Feeders

Dynamics of a Discrete Prey–Predator Model with Mixed Functional Response

2019 ◽  
Vol 29 (14) ◽  
pp. 1950199
Author(s):  
Mohammed Fathy Elettreby ◽  
Aisha Khawagi ◽  
Tamer Nabil
Keyword(s):  
Type I ◽  
Time Behavior ◽  
Stable Fixed Point ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Long Time ◽  
Predator Model ◽  
The Stability

In this paper, we propose a discrete Lotka–Volterra predator–prey model with Holling type-I and -II functional responses. We investigate the stability of the fixed points of this model. Also, we study the effects of changing each control parameter on the long-time behavior of the model. This model contains a lot of complex dynamical behaviors ranging from a stable fixed point to chaotic attractors. Finally, we illustrate the analytical results by some numerical simulations.

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.

Multiple nonfunctional alleles of CCR5 are frequent in various human populations

Blood ◽  
2000 ◽  
Vol 96 (5) ◽  
pp. 1638-1645 ◽  
Author(s):  
Cédric Blanpain ◽  
Benhur Lee ◽  
Marie Tackoen ◽  
Bridget Puffer ◽  
Alain Boom ◽  
...  
Keyword(s):  
Cell Surface ◽  
Receptor Activation ◽  
Human Populations ◽  
Type I ◽  
Binding Affinities ◽  
Functional Responses ◽  
Functional Consequences ◽  
Relative Inability ◽  
Specific Alteration ◽  
Hiv 1

CCR5 is the major coreceptor for macrophage-tropic strains of the human immunodeficiency virus type I (HIV-1). Homozygotes for a 32-base pair (bp) deletion in the coding sequence of the receptor (CCR5Δ32) were found to be highly resistant to viral infection, and CCR5 became, therefore, one of the paradigms illustrating the influence of genetic variability onto individual susceptibility to infectious and other diseases. We investigated the functional consequences of 16 other natural CCR5 mutations described in various human populations. We found that 10 of these variants are efficiently expressed at the cell surface, bind [125I]-MIP-1β with affinities similar to wtCCR5, respond functionally to chemokines, and act as HIV-1 coreceptors. In addition to Δ32, six mutations were characterized by major alterations in their functional response to chemokines, as a consequence of intracellular trapping and poor expression at the cell surface (C101X, FS299), general or specific alteration of ligand binding affinities (C20S, C178R, A29S), or relative inability to mediate receptor activation (L55Q). A29S displayed an unusual pharmacological profile, binding and responding to MCP-2 similarly to wtCCR5, but exhibiting severely impaired binding and functional responses to MIP-1α, MIP-1β, and RANTES. In addition to Δ32, only C101X was totally unable to mediate entry of HIV-1. The fact that nonfunctional CCR5 alleles are relatively frequent in various human populations reinforces the hypothesis of a selective pressure favoring these alleles.

Sign in / Sign up

Export Citation Format

Share Document