Impact of the fear effect in a prey-predator model incorporating a prey refuge

2019 ◽  
Vol 356 ◽  
pp. 328-337 ◽  
Author(s):  
Huisen Zhang ◽  
Yongli Cai ◽  
Shengmao Fu ◽  
Weiming Wang
Keyword(s):  
Prey Refuge ◽  
Fear Effect ◽  
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.

Modeling the Effect of Fear in a Prey–Predator System with Prey Refuge and Gestation Delay

2019 ◽  
Vol 29 (14) ◽  
pp. 1950195 ◽  
Author(s):  
Ankit Kumar ◽  
Balram Dubey
Keyword(s):  
Hopf Bifurcation ◽  
Prey Population ◽  
Reproduction Rate ◽  
Predator Population ◽  
Maximum Lyapunov Exponent ◽  
Stable Limit ◽  
Prey Refuge ◽  
Gestation Delay ◽  
Fear Effect ◽  
Predator System

Recently, some field experiments and studies show that predators affect prey not only by direct killing, they induce fear in prey which reduces the reproduction rate of prey species. Considering this fact, we propose a mathematical model to study the fear effect and prey refuge in prey–predator system with gestation time delay. It is assumed that prey population grows logistically in the absence of predators and the interaction between prey and predator is followed by Crowley–Martin type functional response. We obtained the equilibrium points and studied the local and global asymptotic behaviors of nondelayed system around them. It is observed from our analysis that the fear effect in the prey induces Hopf-bifurcation in the system. It is concluded that the refuge of prey population under a threshold level is lucrative for both the species. Further, we incorporate gestation delay of the predator population in the model. Local and global asymptotic stabilities for delayed model are carried out. The existence of stable limit cycle via Hopf-bifurcation with respect to delay parameter is established. Chaotic oscillations are also observed and confirmed by drawing the bifurcation diagram and evaluating maximum Lyapunov exponent for large values of delay parameter.

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.

Prey–predator model for optimal harvesting with functional response incorporating prey refuge

2015 ◽  
Vol 09 (01) ◽  
pp. 1650014 ◽  
Author(s):  
G. S. Mahapatra ◽  
P. Santra
Keyword(s):  
Functional Response ◽  
System Parameter ◽  
Optimal Harvesting ◽  
Functional Responses ◽  
Prey Refuge ◽  
Numerical Examples ◽  
Pictorial Presentation ◽  
Constant Form ◽  
Predator Model ◽  
Predator System

This paper presents a prey–predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey–predator system parameter.

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