scholarly journals The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

2021 ◽  
pp. 639-657
Author(s):  
Ekhlas Abd Al-Husain Jabr ◽  
Dahlia Khaled Bahlool
Keyword(s):  
Food Web ◽  
Equilibrium Points ◽  
Uniform Boundedness ◽  
Prey Refuge ◽  
Stable Point ◽  
Predator Species ◽  
Periodic Dynamics ◽  
The Web ◽  
Food Web Model

This paper aims to study the role of a prey refuge that depends on both prey and predator species on the dynamics of a food web model. It is assumed that the food transfer among the web levels occurs according to Lotka-Volterra functional response. The solution properties, such as existence, uniqueness, and uniform boundedness, are discussed. The local, as well as the global, stabilities of the solution of the system are investigated. The persistence of the system is studied with the assistance of average Lyapunov function. The local bifurcation conditions that may occur near the equilibrium points are established. Finally, numerical simulation is used to confirm our obtained results. It is observed that the system has only one type of attractors that is a stable point, while periodic dynamics do not exist even on the boundary planes.

scholarly journals Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Huda Abdul Satar ◽  
Raid Kamel Naji
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Food Web ◽  
Equilibrium Points ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Stability And Bifurcation ◽  
Periodic Dynamics ◽  
The Stability ◽  
Food Web Model

In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

scholarly journals The effect of prey refuge on the dynamics of three species food web system

2021 ◽  
Vol 14 (2) ◽  
pp. 105-121
Author(s):  
Dawit Melese ◽  
Abraha Hailu
Keyword(s):  
Numerical Simulation ◽  
Food Web ◽  
Equilibrium Points ◽  
Existence Condition ◽  
Prey Refuge ◽  
Predator Species ◽  
Web System ◽  
Analytical Result ◽  
Type Ii Functional Response ◽  
Linearization Techniques

In this paper, a mathematical model is proposed to study the effect of prey refuge on the dynamics of three species food web system. The food web comprises of a single prey and two competing predators. The two predators predate their prey following Holling type II functional response. In this work we discussed boundedness of the system, existence condition of the equilibrium points and the Jacobean matrix is obtained by linearization techniques. The local stability of the equilibrium points was discussed by using Routh-Hurwitz criteria and the global stability of the equilibrium points by constructing suitable Lyapunov function. Numerical simulation is conducted to support the analytical result. Finally, the effect of prey refuge on the dynamics of one prey two predator was discussed based on the analytical and numerical simulation results. From the numerical simulations, it is found that the dynamical system is persistent for a small value of the refuge constant. However, an increase in the refuge constant leads to the extinction of one of the predator species.

scholarly journals Role of detritus in a spatial food web model with diffusion

2014 ◽  
Vol 89 (5) ◽  
Author(s):  
Andrzej Pękalski ◽  
Janusz Szwabiński
Keyword(s):  
Food Web ◽  
Food Web Model

Developing a high taxonomic resolution food web model to assess the functional role of forage fish in the California Current ecosystem

2016 ◽  
Vol 335 ◽  
pp. 87-100 ◽  
Author(s):  
Laura E. Koehn ◽  
Timothy E. Essington ◽  
Kristin N. Marshall ◽  
Isaac C. Kaplan ◽  
William J. Sydeman ◽  
...  
Keyword(s):  
Food Web ◽  
Functional Role ◽  
California Current ◽  
Taxonomic Resolution ◽  
Forage Fish ◽  
Food Web Model

scholarly journals Theoretical Analysis of an Imprecise Prey-Predator Model with Harvesting and Optimal Control

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Anjana Das ◽  
M. Pal
Keyword(s):  
Complex Dynamics ◽  
Equilibrium Points ◽  
Uniform Boundedness ◽  
Optimal Harvesting ◽  
Model Parameters ◽  
Predator Species ◽  
Proposed Model ◽  
Existence And Stability ◽  
Predator Model ◽  
Predator System

In our present paper, we formulate and study a prey-predator system with imprecise values for the parameters. We also consider harvesting for both the prey and predator species. Then we describe the complex dynamics of the proposed model system including positivity and uniform boundedness of the system, and existence and stability criteria of various equilibrium points. Also the existence of bionomic equilibrium and optimal harvesting policy are thoroughly investigated. Some numerical simulations have been presented in support of theoretical works. Further the requirement of considering imprecise values for the set of model parameters is also highlighted.

Dynamics of a Predator–Prey Model with Holling Type II Functional Response Incorporating a Prey Refuge Depending on Both the Species

2019 ◽  
Vol 20 (1) ◽  
pp. 89-104 ◽  
Author(s):  
Hafizul Molla ◽  
Md. Sabiar Rahman ◽  
Sahabuddin Sarwardi
Keyword(s):  
Hopf Bifurcation ◽  
Uniform Boundedness ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Species ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Predator Model ◽  
The Stability ◽  
Manifold Theory

AbstractWe propose a mathematical model for prey–predator interactions allowing prey refuge. A prey–predator model is considered in the present investigation with the inclusion of Holling type-II response function incorporating a prey refuge depending on both prey and predator species. We have analyzed the system for different interesting dynamical behaviors, such as, persistent, permanent, uniform boundedness, existence, feasibility of equilibria and their stability. The ranges of the significant parameters under which the system admits a Hopf bifurcation are investigated. The system exhibits Hopf-bifurcation around the unique interior equilibrium point of the system. The explicit formula for determining the stability, direction and periodicity of bifurcating periodic solutions are also derived with the use of both the normal form and the center manifold theory. The theoretical findings of this study are substantially validated by enough numerical simulations. The ecological implications of the obtained results are discussed as well.

NETWORK ANALYSIS OF A BENTHIC FOOD WEB MODEL OF A PARTLY RECLAIMED ISLAND IN THE SUNDARBAN MANGROVE ECOSYSTEM, INDIA

2000 ◽  
Vol 08 (03) ◽  
pp. 263-278 ◽  
Author(s):  
SANTANU RAY ◽  
ROBERT E. ULANOWICZ ◽  
N. C. MAJEE ◽  
A. B. ROY
Keyword(s):  
Network Analysis ◽  
Food Web ◽  
Anthropogenic Impacts ◽  
Mangrove Ecosystem ◽  
Large Contribution ◽  
Total System ◽  
Sundarban Mangrove ◽  
System Input ◽  
Food Web Model

Network analysis is performed on a 14 species food web model of the ecosystem occupying a mudflat on a partly reclaimed island of the Sundarban mangrove ecosystem. The results demonstrate a dramatic difference between this heavily impacted mangrove ecosystem in its modes of primary and secondary production and its diminished role of detritus vis-a-vis its less disturbed counterparts. Unlike most benthic mangrove systems, the Sundarban bottom community receives a large contribution from the phytoplankton populations. In this system herbivory and detritivory are virtually equal, in contrast to the usual herbivory:detritivory ratio of 1:5. Anthropogenic impacts have changed the physiography of this system so as to increase the relative importance of zooplankton and meiobenthos as herbivores. Although a slight degree of omnivory is exhibited by the populations of larger organisms, all flows of each integer of trophic length into a food chain may be aggregated that represents the underlying trophic status of the starting food web. Only a small number of pathways of recycle can be identified (31), and the Finn cycling index for this system is quite low (8.4%). Litterfall comprises only 16% of the total system input, which is very little in comparison with most mangrove systems. Pathway redundancy is rather high in this ecosystem, indicating that the surviving system is probably highly resilient to further perturbations, as one might expect for a highly impacted system.

scholarly journals The Dynamics of Food Web Model with Defensive Switching Property

2008 ◽  
Vol 13 (2) ◽  
pp. 225-240 ◽  
Author(s):  
R. K. Naji ◽  
I. H. Kasim
Keyword(s):  
Equilibrium Point ◽  
Food Web ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Globally Asymptotically Stable ◽  
Predator Species ◽  
Trivial Equilibrium ◽  
The Stability ◽  
Parameter Values ◽  
Food Web Model

In this paper, a food web model consisting of two-predator one-prey with the defensive switching of predation avoidance is proposed and analyzed. It is assumed that the prey growth logistically in the absence of predators and defends itself from relatively abundant predator species by switching to another habitat with relatively rare predator species. Sufficient conditions for the stability of the non-trivial equilibrium point are obtained. The Lyapunov function is constructed to establish the global asymptotic stability of the non-trivial equilibrium point when the intensity of defensive switching equal one. Numerical simulations for different sets of parameter values and for different sets of initial conditions are carried out. It has been shown that the system has a globally asymptotically stable non-trivial point when the two predators have the same mortality rates.

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