Fear effect on a discrete-time prey predator model with imprecise biological parameters

2020 ◽  
Author(s):  
Dipankar Ghosh ◽  
Prasun Kumar Santra ◽  
G. S. Mahapatra
Keyword(s):  
Discrete Time ◽  
Biological Parameters ◽  
Fear Effect ◽  
Predator Model

DYNAMICAL STUDY OF DISCRETE-TIME PREY–PREDATOR MODEL WITH CONSTANT PREY REFUGE UNDER IMPRECISE BIOLOGICAL PARAMETERS

2020 ◽  
Vol 28 (03) ◽  
pp. 681-699
Author(s):  
P. K. SANTRA ◽  
G. S. MAHAPATRA
Keyword(s):  
Discrete Time ◽  
Discrete Model ◽  
Prey Species ◽  
Complex Nature ◽  
Biological Parameters ◽  
Constant Number ◽  
Prey Refuge ◽  
Dynamical Study ◽  
Dynamical Properties ◽  
Predator Model

The objective of this paper is to study the dynamical properties of a discrete-time prey–predator model under imprecise biological parameters. We consider refuge for prey species as a constant number. The equilibria of the model are obtained, and the dynamic behaviors of the proposed system are examined for the interval biological parameters. Simulations of the model are performed for different parameters of the model. Numerical simulations demonstrate that the proposed discrete model exhibits rich dynamics of a chaotic and complex nature.

scholarly journals The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 865
Author(s):  
Jialin Chen ◽  
Xiaqing He ◽  
Fengde Chen
Keyword(s):  
Discrete Time ◽  
Food Resource ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Predator Species ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Fear Effect ◽  
Prey System ◽  
Trivial Equilibrium

A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.

Dynamics and bifurcations of a discrete-time prey-predator model with Allee effect on the prey population

2021 ◽  
Vol 48 ◽  
pp. 100962
Author(s):  
Z. Eskandari ◽  
J. Alidousti ◽  
Z. Avazzadeh ◽  
J.A. Tenreiro Machado
Keyword(s):  
Discrete Time ◽  
Allee Effect ◽  
Prey Population ◽  
Predator Model

scholarly journals Fear effect in discrete prey-predator model incorporating square root functional response

2021 ◽  
Vol 2 (2) ◽  
pp. 51-57
Author(s):  
P.K. Santra
Keyword(s):  
Functional Response ◽  
Stability Condition ◽  
Discrete Model ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Square Root ◽  
Bifurcation Diagrams ◽  
Fear Effect ◽  
Hypothetical Data ◽  
Predator Model

In this work, an interaction between prey and its predator involving the effect of fear in presence of the predator and the square root functional response is investigated. Fixed points and their stability condition are calculated. The conditions for the occurrence of some phenomena namely Neimark-Sacker, Flip, and Fold bifurcations are given. Base on some hypothetical data, the numerical simulations consist of phase portraits and bifurcation diagrams are demonstrated to picturise the dynamical behavior. It is also shown numerically that rich dynamics are obtained by the discrete model as the effect of fear.

EFFECT OF TIME-DELAY ON A PREY–PREDATOR MODEL WITH MICROPARASITE INFECTION IN THE PREDATOR

2011 ◽  
Vol 19 (02) ◽  
pp. 365-387 ◽  
Author(s):  
SWETA PATHAK ◽  
ALAKES MAITI ◽  
SHYAM PADA BERA
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Predator Population ◽  
Dynamical Characteristics ◽  
Dynamical Behaviors ◽  
Discrete Time Delay ◽  
Mathematical Analyses ◽  
Predator Model ◽  
Living Organisms

To increase a prey population that is attacked by a predator it is more convenient and economical to choose the living organisms to control the predator. In this paper, the dynamical behaviors of a prey–predator model with microparasitic infection in the predator have been discussed. In this epidemiological model the microparasite is horizontally transmitted and attacks the predator population only. The infected population does not recover or become immune. The dynamical characteristics of the system are studied through mathematical analyses. The role of discrete time-delay has been discussed to show that time-delay can induce instability and oscillation. Numerical simulations are carried out. Biological implications have been discussed.

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