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 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 Dynamic Behaviors of a Nonautonomous Discrete Predator-Prey System Incorporating a Prey Refuge and Holling Type II Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Wanlin Chen ◽  
Yuhua Lin
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Type Ii Functional Response

A nonautonomous discrete predator-prey system incorporating a prey refuge and Holling type II functional response is studied in this paper. A set of sufficient conditions which guarantee the persistence and global stability of the system are obtained, respectively. Our results show that if refuge is large enough then predator species will be driven to extinction due to the lack of enough food. Two examples together with their numerical simulations show the feasibility of the main results.

scholarly journals The Dynamics of a Tritrophic Leslie-Gower Food-Web System with the Effect of Fear

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Firas Hussean Maghool ◽  
Raid Kamel Naji
Keyword(s):  
Food Web ◽  
Evolutionary Biology ◽  
Basin Of Attraction ◽  
Growth Function ◽  
Generalist Predator ◽  
Specific Level ◽  
Predator Species ◽  
Web System ◽  
Group Defense ◽  
The Impact

The avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels. It is assumed that the generalist predator grows logistically using the Leslie-Gower type of growth function. All the solution properties of the model are studied. Local dynamics behaviors are investigated. The basin of attraction for each equilibrium is determined using the Lyapunov function. The conditions of persistence of the model are specified. The study of local bifurcation in the model is done. Numerical simulations are implemented to show the obtained results. It is watched that the system is wealthy in its dynamics including chaos. The fear factor works as a stabilizing factor in the system up to a specific level; otherwise, it leads to the extinction of the predator. However, increasing the prey’s group defense leads to extinction in predator species.

scholarly journals Global Dynamics of an Exploited Prey-Predator Model with Constant Prey Refuge

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Uttam Das ◽  
T. K. Kar ◽  
U. K. Pahari
Keyword(s):  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Global Dynamics ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Species ◽  
Interior Equilibrium ◽  
Predator Model ◽  
Theoretical Results ◽  
Type Ii Functional Response

This paper describes a prey-predator model with Holling type II functional response incorporating constant prey refuge and harvesting to both prey and predator species. We have analyzed the boundedness of the system and existence of all possible feasible equilibria and discussed local as well as global stabilities at interior equilibrium of the system. The occurrence of Hopf bifurcation of the system is examined, and it was observed that the bifurcation is either supercritical or subcritical. Influences of prey refuge and harvesting efforts are also discussed. Some numerical simulations are carried out for the validity of theoretical results.

scholarly journals Stability of Cancerous Chemotherapy Model with Obesity Effect

CAUCHY ◽  
2019 ◽  
Vol 5 (4) ◽  
pp. 186
Author(s):  
Indah Yanti ◽  
Ummu Habibah
Keyword(s):  
Numerical Simulation ◽  
Cancer Cells ◽  
Immune Cells ◽  
Population Model ◽  
Equilibrium Points ◽  
Fat Cells ◽  
Normal Cells ◽  
Total Cancer ◽  
Analytical Result ◽  
Coexistence Equilibrium

<p class="Body">In this paper we present stability of cancerous chemotherapy model with obesity effect. This is a four-population model that includes immune cells, cancer cells, normal cells, and fat cells. The analytical result shows that there are four equilibrium points in case the drugs given and fat cells were not equal to zero, i.e., dead equilibrium, total cancer invasion equilibrium, cancer-free equilibrium, and coexistence equilibrium. Some numerical simulation also presented to illustrate the results.</p>

Stability and Hopf Bifurcation of a Delayed Prey–Predator Model with Disease in the Predator

2019 ◽  
Vol 29 (07) ◽  
pp. 1950091 ◽  
Author(s):  
Chuangxia Huang ◽  
Hua Zhang ◽  
Jinde Cao ◽  
Haijun Hu
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Mass Action ◽  
Functional Responses ◽  
Predator Species ◽  
Interior Equilibrium ◽  
Positivity Of Solutions ◽  
Predator Model ◽  
The Stability ◽  
Type Ii Functional Response

Dealing with the epidemiological prey–predator is very important for us to understand the dynamical characteristics of population models. The existing literature has shown that disease introduction into the predator group can destabilize the established prey–predator communities. In this paper, we establish a new delayed SIS epidemiological prey–predator model with the assumptions that the disease is transmitted among the predator species only and different type of predators have different functional responses, viz. the infected predator consumes the prey according to Holling type-II functional response and the susceptible predator consumes the prey following the law of mass action. The positivity of solutions, the existence of various equilibrium points, the stability and bifurcation at those equilibrium points are investigated at length. Using the incubation period as bifurcation parameter, it is observed that a Hopf bifurcation may occur around the equilibrium points when the parameter passes through some critical values. We also discuss the direction and stability of the Hopf bifurcation around the interior equilibrium point. Simulations are arranged to show the correctness and effectiveness of these theoretical results.

scholarly journals Dynamical Analysis Predator-Prey Population with Holling Type II Functional Response

2021 ◽  
Author(s):  
FE. Universitas Andi Djemma
Keyword(s):  
Functional Response ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Type Ii Functional Response

In this article, we investigate the dynamical analysis of predator prey model. Interactionamong preys and predators use Holling type II functional response, and assuming prey refuge aswell as harvesting in both populations. This study aims to study the predator prey model and todetermine the effect of overharvesting which consequently will affect the ecosystem. In the modelfound three equilibrium points, i.e., (0,0) is the extinction of predator and prey equilibrium,?(??, 0) is the equilibrium with predatory populations extinct and the last equilibrium points?(??, ??) is the coexist equilibrium. All equilibrium points are asymptotically stable (locally) undercertain conditions. These analytical findings were confirmed by several numerical simulations.

scholarly journals Evidence for Ecosystem-Level Trophic Cascade Effects Involving Gulf Menhaden (Brevoortia patronus) Triggered by the Deepwater Horizon Blowout

2021 ◽  
Vol 9 (2) ◽  
pp. 190
Author(s):  
Jeffrey Short ◽  
Christine Voss ◽  
Maria Vozzo ◽  
Vincent Guillory ◽  
Harold Geiger ◽  
...  
Keyword(s):  
Food Web ◽  
Mississippi River ◽  
Trophic Cascade ◽  
Oil Spills ◽  
Net Primary Production ◽  
Spatial Scales ◽  
Dominant Role ◽  
Deepwater Horizon ◽  
Predator Species ◽  
Brevoortia Patronus

Unprecedented recruitment of Gulf menhaden (Brevoortia patronus) followed the 2010 Deepwater Horizon blowout (DWH). The foregone consumption of Gulf menhaden, after their many predator species were killed by oiling, increased competition among menhaden for food, resulting in poor physiological conditions and low lipid content during 2011 and 2012. Menhaden sampled for length and weight measurements, beginning in 2011, exhibited the poorest condition around Barataria Bay, west of the Mississippi River, where recruitment of the 2010 year class was highest. Trophodynamic comparisons indicate that ~20% of net primary production flowed through Gulf menhaden prior to the DWH, increasing to ~38% in 2011 and ~27% in 2012, confirming the dominant role of Gulf menhaden in their food web. Hyperabundant Gulf menhaden likely suppressed populations of their zooplankton prey, suggesting a trophic cascade triggered by increased menhaden recruitment. Additionally, low-lipid menhaden likely became “junk food” for predators, further propagating adverse effects. We posit that food web analyses based on inappropriate spatial scales for dominant species, or solely on biomass, provide insufficient indication of the ecosystem consequences of oiling injury. Including such cascading and associated indirect effects in damage assessment models will enhance the ability to anticipate and estimate ecosystem damage from, and provide recovery guidance for, major oil spills.

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

Sign in / Sign up

Export Citation Format

Share Document