scholarly journals An Extension of Two Species Lotka-Volterra Competition Model

2021 ◽  
Vol 8 (2) ◽  
pp. 90
Author(s):  
Idy BA ◽  
Papa Ibrahima NDIAYE ◽  
Mahe Ndao ◽  
AboubaKary Diakhaby
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Competition Model ◽  
Complete Analysis ◽  
Species Competition ◽  
Planar System ◽  
Saddle Node Bifurcation ◽  
Competitive Effects ◽  
Competition Effects ◽  
Competitive Species

Limiting resource is a angular stone of the interactions between species in ecosystems such as competition, prey-predators and food chain systems. In this paper, we propose a planar system as an extension of Lotka-Voterra competition model. This describes? two competitive species for a single resource? which are affected by intra and inter-specific interference. We give its complete analysis for the existence and local stability of all equlibria and some conditions of global stability. The model exhibits a rich set of behaviors with a multiplicity of coexistence equilibria, bi-stability, tri-stability and occurrence of global stability of the exclusion of one species and the coexistence? equilibrium. The asymptotic behavior and the number of coexistence equilibria are shown by a saddle-node bifurcation of the level of resource under conditions on competitive effects relatively to associated growth rate per unit of resource.Moreover, we determine the competition outcome in the situations of Balanced and Unbalanced intra-inter species competition effects. Finally, we illustrate results by numerical simulations.

scholarly journals A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
G. P. Samanta
Keyword(s):  
Planck Equation ◽  
Competition Model ◽  
Probability Density Functions ◽  
Density Functions ◽  
Species Competition ◽  
Symmetric Competition ◽  
Competitive Species ◽  
The Stability ◽  
The Relationship ◽  
Nonequilibrium Fluctuation

The object of this paper is to study the stability behaviours of the deterministic and stochastic versions of a two-species symmetric competition model. The logistic parameters of the competitive species are perturbed by colored noises or Ornstein-Uhlenbeck processes due to random environment. The Fokker-Planck equation has been used to obtain probability density functions. Here, we have also discussed the relationship between stability behaviours of this model in a deterministic environment and the corresponding model in a stochastic environment.

scholarly journals Local stability implies global stability for the planar Ricker competition model

2014 ◽  
Vol 19 (2) ◽  
pp. 323-351 ◽  
Author(s):  
E. Cabral Balreira ◽  
◽  
Saber Elaydi ◽  
Rafael Luís ◽  
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Competition Model

scholarly journals Existence and Local Stability of Stationary Solutions for Nonlinear Gilpin Ayala Competition Model with Dirichlet Boundary Value

2020 ◽  
Author(s):  
Ruofeng Rao
Keyword(s):  
Stability Criterion ◽  
Local Stability ◽  
Dirichlet Boundary ◽  
Stationary Solutions ◽  
Competition Model ◽  
Mountain Pass Lemma ◽  
Species Competition ◽  
Diffusion Behavior ◽  
Population Extinction ◽  
Lyapunov Function Method

In this paper, the existence of two nontrivial stationary solutions for the nonlinear Gilpin Ayala two species competition model is given by using the mountain pass lemma, and the local stability criterion of the trivial solution is given by using Lyapunov function method. Based on the local stability criterion, we give some suggestions on how to avoid the population extinction. This is, when the population is on the verge of extinction, we should try our best to avoid the diffusion behavior and reduce the diffusion coefficient, otherwise the species are easy to go extinct. Numerical example shows the effectiveness of the proposed method.

scholarly journals Competition Model in a Chemostat with Monotone Functional Response

1970 ◽  
Vol 30 ◽  
pp. 100-110
Author(s):  
SM Sohel Rana
Keyword(s):  
Population Dynamics ◽  
Global Stability ◽  
Key Words ◽  
Functional Response ◽  
Local Stability ◽  
Competition Model ◽  
Time Stability ◽  
Key Words Competition ◽  
Key Points ◽  
Two Populations

 In this paper, a model for competition of two populations of microorganisms in a chemostat with monotone functional response is considered. We prove that the solutions are positive and bounded for all time. Stability of nonnegative equilibria and persistence of solutions are presented. Graphical results are also given to help illustrate the key points in the population dynamics of the model. Key words: competition; local stability; global stability; persistence. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 100-110  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8507

scholarly journals Operating diagram of a flocculation model in the chemostat

2020 ◽  
Vol Volume 31 - 2019 - CARI 2018 ◽  
Author(s):  
Radhouane Fekih-Salem ◽  
Tewfik Sari
Keyword(s):  
Local Stability ◽  
Stability Region ◽  
Steady States ◽  
Complete Analysis ◽  
Stable Limit ◽  
Control Parameters ◽  
Coexistence Region ◽  
Microbial Ecosystem ◽  
International Audience ◽  
Stable Limit Cycles

International audience The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species. L'objectif de cette étude est d'analyser un modèle du chémostat impliquant la dynamique d'attachement et de détachement de la biomasse planctonique et agrégée en présence d'une seule ressource. En considérant la mortalité des espèces, nous donnons une analyse complète de l'existence et de la stabilité locale de tous les équilibres pour des taux de croissance monotones. Le modèle pré-sente un ensemble riche de comportements avec multiplicité d'équilibres de coexistence, bi-stabilité et apparition des cycles limites stables. De plus, nous déterminons le diagramme opératoire qui dé-crit le comportement asymptotique du système par rapport aux paramètres de contrôle. Il montre l'émergence d'une région de bi-stabilité via une bifurcation noeud col et l'occurrence d'une région de coexistence via une bifurcation transcritique. Enfin, nous illustrons l'importance de la mortalité sur la déstabilisation de l'écosystème microbien en favorisant le lessivage des espèces.

scholarly journals A Stochastic Model for Three Species

2018 ◽  
Vol 7 (4.10) ◽  
pp. 497
Author(s):  
Y. Suresh Kumar ◽  
N. Seshagiri Rao ◽  
B. V AppaRao
Keyword(s):  
Stochastic Process ◽  
Stochastic Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Limited Resources

The present work is related to a three species ecosystem including a mutualism interaction between two species and a predator, where the predator is depending on both the mutual species. All three species in this model are considered in limited resources. The sustainability of the system (local stability) is discussed through the perturbed technique at the possible existing each equilibrium points. Using Lyapunov's technique the global stability of the system is also described. Further the nature of the system is observed by introducing the stochastic process to the species and the numerical simulations are studied to know the interaction among the species. 

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