A nullcline approach to global stability in discrete-time predator–prey models

2021 ◽  
pp. 1-14
Author(s):  
Azmy S. Ackleh ◽  
Paul Salceanu ◽  
Amy Veprauskas
Keyword(s):  
Global Stability ◽  
Discrete Time ◽  
Predator Prey ◽  
Predator Prey Models

scholarly journals Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Wahiba Khellaf ◽  
Nasreddine Hamri
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Qualitative Behavior ◽  
Uniform Persistence ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Prey System ◽  
Predator Prey Models ◽  
Type Ii Functional Response

We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.

Hydra effect and paradox of enrichment in discrete-time predator-prey models

2019 ◽  
Vol 310 ◽  
pp. 120-127 ◽  
Author(s):  
Vinicius Weide ◽  
Maria C. Varriale ◽  
Frank M. Hilker
Keyword(s):  
Discrete Time ◽  
Predator Prey ◽  
Paradox Of Enrichment ◽  
Hydra Effect ◽  
Predator Prey Models

scholarly journals Global Stability of a Predator-Prey Model with Ivlev-Type Functional Response

2020 ◽  
Vol 99 (99) ◽  
pp. 1-12
Author(s):  
Yinshu Wu ◽  
Wenzhang Huang
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Local Stability ◽  
Positive Equilibrium ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Prey Models ◽  
Global And Local

A predator-prey model with Ivlev-Type functional response is studied. The main purpose is to investigate the global stability of a positive (co-existence) equilibrium, whenever it exists. A recently developed approach shows that for certain classes of models, there is an implicitly defined function which plays an important rule in determining the global stability of the positive equilibrium. By performing a detailed analytic analysis we demonstrate that a crucial property of this implicitly defined function is governed by the local stability of the positive equilibrium, which enable us to show that the global and local stability of the positive equilibrium, whenever it exists, is equivalent. We believe that our approach can be extended to study the global stability of the positive equilibrium for predator-prey models with some other types of functional responses.

scholarly journals A Lyapunov Function and Global Stability for a Class of Predator-Prey Models

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaoqin Wang ◽  
Huihai Ma
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Equilibrium States ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Predator Prey Models

We construct a new Lyapunov function for a class of predation models. Global stability of the positive equilibrium states of these systems can be established when the Lyapunov function is used.

scholarly journals The Stability of Gauss Model Having One-Prey and Two-Predators

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
A. Farajzadeh ◽  
M. H. Rahmani Doust ◽  
F. Haghighifar ◽  
D. Baleanu
Keyword(s):  
Mathematical Biology ◽  
Global Stability ◽  
Equilibrium Points ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Stability Properties ◽  
Interacting Species ◽  
Predator Prey Models ◽  
The Stability

The study of the dynamics of predator-prey interactions can be recognized as a major issue in mathematical biology. In the present paper, some Gauss predator-prey models in which three ecologically interacting species have been considered and the behavior of their solutions in the stability aspect have been investigated. The main aim of this paper is to consider the local and global stability properties of the equilibrium points for represented systems. Finally, stability of some examples of Gauss model with one prey and two predators is discussed.

Sign in / Sign up

Export Citation Format

Share Document