scholarly journals A prey-predator model with infection in both prey and predator

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1753-1767 ◽  
Author(s):  
S.P. Bera ◽  
A. Maiti ◽  
G.P. Samanta
Keyword(s):  
Differential Equation ◽  
Computer Simulations ◽  
Equilibrium Points ◽  
Predator Model ◽  
Predator System

This paper aims to study the dynamical behaviours of a prey-predator system where both prey and predator populations are affected by diseases. A system of four differential equation has been proposed and analyzed. Stability of the equilibrium points of the model has been investigated. Computer simulations are carried out to illustrate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.

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.

STABILITY ANALYSIS OF A PREY-PREDATOR MODEL WITH DELAY AND HARVESTING

2004 ◽  
Vol 12 (01) ◽  
pp. 61-71 ◽  
Author(s):  
TAPAN KUMAR KAR
Keyword(s):  
Stability Analysis ◽  
Computer Simulations ◽  
Significant Role ◽  
Combined Effects ◽  
Predator Model ◽  
The Stability ◽  
Predator System

An analysis is presented for a model of a two species prey-predator system subject to the combined effects of delay and harvesting. Our study shows that, both the delay and harvesting effort may play a significant role on the stability of the system. Computer simulations are carried out to explain some of the mathematical conclusions.

scholarly journals The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Raid Kamel Naji ◽  
Salam Jasim Majeed
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Stage Structure ◽  
Dynamical Analysis ◽  
Local Bifurcation ◽  
Structure Population ◽  
Global Stability Analysis ◽  
Proposed Model ◽  
Predator Model ◽  
Predator System

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.

A STUDY OF BIFURCATION OF PREY–PREDATOR MODEL WITH TIME DELAY AND HARVESTING USING FUZZY PARAMETERS

2018 ◽  
Vol 26 (02) ◽  
pp. 339-372 ◽  
Author(s):  
D. PAL ◽  
G. S. MAHAPATRA ◽  
G. P. SAMANTA
Keyword(s):  
Time Delay ◽  
Equilibrium Points ◽  
Fuzzy Model ◽  
Solution Procedure ◽  
Distance Method ◽  
Gestation Delay ◽  
Fuzzy Environment ◽  
Predator Model ◽  
The Stability ◽  
Predator System

In this work, a fuzzy prey–predator system with time delay is proposed. The model consists of two preys and one predator. The biological coefficients/parameters are considered as imprecise in nature and quantified by triangular fuzzy numbers. We have studied the effect of gestation delay on the stability of the system in fuzzy environment. The signed distance method for the defuzzification of the proposed fuzzy prey–predator system is adopted. For the underlying fuzzy model, we have provided a solution procedure to find all possible equilibrium points and studied their stabilities in the fuzzy sense. It is observed that there are stability switches, and Hopf-bifurcation occurs when the delay crosses some critical value in fuzzy sense. Numerical illustrations are provided in crisp as well as fuzzy environment with the help of graphical presentations to support our proposed approach.

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.

scholarly journals A Mathematical Study on a Diseased Prey-Predator Model with Predator Harvesting

2020 ◽  
Vol 8 (2) ◽  
Author(s):  
Srinivasarao Thota
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Local Stability ◽  
Equilibrium Points ◽  
Mathematical Study ◽  
First Order ◽  
Predator Model ◽  
Predator System ◽  
Infected Prey ◽  
First Order Differential Equations

 In this paper, we present a mathematical model for a prey-predator system with infectious disease in the prey population. We assumed that there is harvesting from the predator and a defensive property against predation. This model is constituted by a system of nonlinear decoupled ordinary first order differential equations, which describe the interaction among the healthy prey, infected prey and predator. The existence, uniqueness and boundedness of the system solutions are investigated. Local stability of the system at equilibrium points is discussed.  

scholarly journals A Study of a Diseased Prey-Predator Model with Refuge in Prey and Harvesting from Predator

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Ahmed Sami Abdulghafour ◽  
Raid Kamel Naji
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Equilibrium Points ◽  
Nonlinear Ordinary Differential Equations ◽  
First Order ◽  
Persistence Conditions ◽  
System Solution ◽  
Predator Model ◽  
Predator System ◽  
Infected Prey

In this paper, a mathematical model of a prey-predator system with infectious disease in the prey population is proposed and studied. It is assumed that there is a constant refuge in prey as a defensive property against predation and harvesting from the predator. The proposed mathematical model is consisting of three first-order nonlinear ordinary differential equations, which describe the interaction among the healthy prey, infected prey, and predator. The existence, uniqueness, and boundedness of the system’ solution are investigated. The system's equilibrium points are calculated with studying their local and global stability. The persistence conditions of the proposed system are established. Finally the obtained analytical results are justified by a numerical simulation.

scholarly journals The Dynamics of A Square Root Prey-Predator Model with Fear

2020 ◽  
pp. 139-146
Author(s):  
Nabaa Hassain Fakhry ◽  
Raid Kamel Naji
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Global Dynamics ◽  
Local Bifurcation ◽  
Square Root ◽  
Predator Species ◽  
Local Bifurcation Analysis ◽  
Predator Model ◽  
The Stability ◽  
Predator System

An ecological model consisting of prey-predator system involving the prey’s fear is proposed and studied. It is assumed that the predator species consumed the prey according to prey square root type of functional response. The existence, uniqueness and boundedness of the solution are examined. All the possible equilibrium points are determined. The stability analysis of these points is investigated along with the persistence of the system. The local bifurcation analysis is carried out. Finally, this paper is ended with a numerical simulation to understand the global dynamics of the system.

Parameter uncertainty in biomathematical model described by one-prey two-predator system with mutualism

2017 ◽  
Vol 10 (06) ◽  
pp. 1750082
Author(s):  
D. Pal ◽  
G. S. Mahapatra ◽  
G. P. Samanta
Keyword(s):  
Maximum Principle ◽  
Parameter Uncertainty ◽  
Equilibrium Points ◽  
Optimal Harvesting ◽  
Biological Parameters ◽  
Optimal Conditions ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Predator Model ◽  
Predator System

In this paper, a three-species system consisting of two predators which are in mutualism with each other and preying on the same single prey is considered. Also, the prey and first predator are harvested under optimal conditions. The values of the biological parameters depend on the collection of data from the experts as well as on the nature of the environment in which prey–predator system are considered. So the biological parameters are not precise in reality. This paper presents a different approach to study the prey–predator model with imprecise biological parameters. All the possible equilibrium points are identified and the local as well as global stability criteria under impreciseness are discussed. The possibility of existence of bionomic equilibrium is discussed. The optimal harvesting policy is studied using Pontryagin’s maximum principle. Numerical examples are provided to support the proposed approach.

scholarly journals An Impulsively Controlled Three-Species Prey-Predator Model with Stage Structure and Birth Pulse for Predator

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Yanyan Hu ◽  
Mei Yan ◽  
Zhongyi Xiang
Keyword(s):  
Small Amplitude ◽  
Floquet Theory ◽  
Stage Structure ◽  
Critical Value ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Birth Pulse ◽  
Impulsive Equation ◽  
Predator Model ◽  
Predator System

We investigate the dynamic behaviors of a two-prey one-predator system with stage structure and birth pulse for predator. By using the Floquet theory of linear periodic impulsive equation and small amplitude perturbation method, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we study the permanence of the investigated model. Our results provide valuable strategy for biological economics management. Numerical analysis is also inserted to illustrate the results.

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