Global analysis of a delayed stage structure prey–predator model with Crowley–Martin type functional response

2019 ◽  
Vol 162 ◽  
pp. 58-84 ◽  
Author(s):  
Atasi Patra Maiti ◽  
B. Dubey ◽  
A. Chakraborty
Keyword(s):  
Functional Response ◽  
Global Analysis ◽  
Stage Structure ◽  
Predator Model

scholarly journals The Dynamical Behavior of Stage Structured Prey-Predator Model in the Harvesting and Toxin Presence

2019 ◽  
Vol 54 (6) ◽  
Author(s):  
Azhar Abbas Majeed ◽  
Moayad H. Ismaeel
Keyword(s):  
Mathematical Model ◽  
Functional Response ◽  
Lyapunov Functions ◽  
Numerical Models ◽  
Dynamical Behavior ◽  
Stage Structure ◽  
Suggested Model ◽  
Final Point ◽  
Predator Model ◽  
Predator System

In this study, a mathematical model that consists of a form of prey-predator system with stage structure in the presence of harvesting and toxicity has been proposed and studied by using the classic Lotka-Volterra functional response. The presence, uniqueness, and boundedness resolution of the suggested model are discussed. The steadiness enquiries of all possible stability points tare studied. The global steadiness of these stability points are accomplished by fitting Lyapunov functions. As a final point, numerical models are put through not just for conforming tthe hypothetical results attained, but also to demonstrate the influences of distinction of each factor on the suggested paradigm.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

scholarly journals Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Can-Yun Huang ◽  
Min Zhao ◽  
Hai-Feng Huo
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Ii Functional Response

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

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.

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.

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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