Bifurcation structure of stationary solutions of a Lotka-Volterra competition model with density-dependent diffusion

1998 ◽  
pp. 293-305
Author(s):  
Yukio Kan-on
Keyword(s):  
Stationary Solutions ◽  
Competition Model ◽  
Bifurcation Structure ◽  
Density Dependent

scholarly journals Global Stability of Delayed Ecosystem via Impulsive Differential Inequality and Minimax Principle

2021 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Global Stability ◽  
Stationary Solution ◽  
Differential Inequality ◽  
Impulsive Control ◽  
Stationary Solutions ◽  
Delayed Feedback ◽  
Competition Model ◽  
Minimax Principle ◽  
Impulsive Differential Inequality

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

EFFECTS OF REFUGES AND DENSITY DEPENDENT DISPERSAL ON INTERSPECIFIC COMPETITION DYNAMICS

2012 ◽  
Vol 22 (02) ◽  
pp. 1250029 ◽  
Author(s):  
NGUYEN-NGOC DOANH ◽  
NGUYEN-HUU TRI ◽  
AUGER PIERRE
Keyword(s):  
Interspecific Competition ◽  
Competition Model ◽  
Density Dependent ◽  
First Case ◽  
Global Extinction ◽  
Density Dependent Dispersal ◽  
Effects Of Density

We present a classical interspecific competition model. Individuals compete for a resource on a common patch and can go to a refuge. It is assumed that if species would remain on the competition patch, species 1 survives and species 2 would go extinct. Therefore, species 1 is Locally Superior Competitor (LSC) and species 2 Locally Inferior Competitor (LIC). We study the effects of density dependent dispersal from the competition patch to the refuge on the global outcome of competition. We study two cases. The first case considers LSC density dependent dispersal of the LIC trying to escape competition and going to its refuge when the LSC density is large. The second case considers aggressiveness of LIC leading to LIC density dependent dispersal of the LSC. We show that under some conditions, tactic 2 can allow the LIC to survive and even provoke global extinction of the LSC.

scholarly journals Local and Global Stability Analysis for Gilpin-Ayala Competition Model Involved in Harmful Species Via LMI Approach and Variational Methods

2021 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Variational Methods ◽  
Stability Criterion ◽  
Reaction Diffusion ◽  
Stationary Solutions ◽  
Competition Model ◽  
Mountain Pass Lemma ◽  
Lmi Approach ◽  
Null Solution ◽  
The Stability ◽  
Harmful Species

In this paper, stability of reaction-diffusion Gilpin-Ayala competition model with Dirichlet boundary value, involved in harmful species, was investigated. Employing Mountain Pass Lemma and linear approximation principle results in the local stability criterion of the null solution of the ecosystem which owns at least three stationary solutions. On the other hand, globally asymptotical stability criterion for the null solution of the ecosystem was derived by variational methods and LMI approach. It is worth mentioning that the stability criteria of null solution presented some useful hints on how to eliminate pests and bacteria. Finally, two numerical examples show the effectiveness of the proposed methods.

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