Discrete Prey–Predator Model with Square Root Functional Response Under Imprecise Biological Parameters

2020 ◽  
pp. 211-225
Author(s):  
P. Santra ◽  
G. S. Mahapatra
Keyword(s):  
Functional Response ◽  
Square Root ◽  
Biological Parameters ◽  
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.

STABILITY AND BIFURCATION ANALYSIS OF A DISCRETE PREY–PREDATOR MODEL WITH SQUARE-ROOT FUNCTIONAL RESPONSE AND OPTIMAL HARVESTING

2020 ◽  
Vol 28 (01) ◽  
pp. 91-110
Author(s):  
PRABIR CHAKRABORTY ◽  
UTTAM GHOSH ◽  
SUSMITA SARKAR
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Functional Response ◽  
Population Model ◽  
Optimal Harvesting ◽  
Herd Behavior ◽  
Square Root ◽  
Optimal Harvesting Policy ◽  
Optimal Value ◽  
Predator Model

In this paper, we have considered a discrete prey–predator model with square-root functional response and optimal harvesting policy. This type of functional response is used to study the dynamics of the prey–predator model where the prey population exhibits herd behavior, i.e., the interaction between prey and predator occurs along the boundary of the population. The considered population model has three fixed points; one is trivial, the second one is axial and the last one is an interior fixed point. The first two fixed points are always feasible but the last one depends on the parameter value. The interior fixed point experiences the flip and Neimark–Sacker bifurcations depending on the predator harvesting coefficient. Finally, an optimal harvesting policy has been introduced and the optimal value of the harvesting coefficient is determined.

scholarly journals Discrete-time prey-predator model with θ-logistic growth for prey incorporating square root functional response

2020 ◽  
Vol 1 (2) ◽  
pp. 41-48
Author(s):  
P.K. Santra
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Discrete Model ◽  
Phase Portraits ◽  
Logistic Growth ◽  
Herd Behavior ◽  
Square Root ◽  
Existence And Stability ◽  
Predator Model ◽  
Predator System

This article presents the dynamics of a discrete-time prey-predator system with square root functional response incorporating θ-logistic growth. This type of functional response is used to study the dynamics of the prey--predator system where the prey population exhibits herd behavior, i.e., the interaction between prey and predator occurs along the boundary of the population. The existence and stability of fixed points and Neimark-Sacker Bifurcation (NSB) are analyzed. The phase portraits, bifurcation diagrams and Lyapunov exponents are presented and analyzed for different parameters of the model. Numerical simulations show that the discrete model exhibits rich dynamics as the effect of θ-logistic growth.

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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