scholarly journals Positive solution branches of two-species competition model in open advective environments

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Yan'e Wang ◽  
◽  
Nana Tian ◽  
Hua Nie ◽  
Keyword(s):  
Positive Solution ◽  
Competition Model ◽  
Species Competition

scholarly journals Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Rong Liu ◽  
Guirong Liu
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solution ◽  
Deterministic Model ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Species Competition ◽  
Martingale Inequality ◽  
Interior Equilibrium ◽  
Exponential Martingale ◽  
Global Positive Solution

This paper is concerned with a stochastic two-species competition model under the effect of disease. It is assumed that one of the competing populations is vulnerable to an infections disease. By the comparison theorem of stochastic differential equations, we prove the existence and uniqueness of global positive solution of the model. Then, the asymptotic pathwise behavior of the model is given via the exponential martingale inequality and Borel-Cantelli lemma. Next, we find a new method to prove the boundedness of the pth moment of the global positive solution. Then, sufficient conditions for extinction and persistence in mean are obtained. Furthermore, by constructing a suitable Lyapunov function, we investigate the asymptotic behavior of the stochastic model around the interior equilibrium of the deterministic model. At last, some numerical simulations are introduced to justify the analytical results. The results in this paper extend the previous related results.

Dynamics of an autonomous Gilpin–Ayala competition model with random perturbation

2021 ◽  
pp. 2050043
Author(s):  
Jing Fu ◽  
Qixing Han ◽  
Daqing Jiang ◽  
Yanyan Yang
Keyword(s):  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Necessary Conditions ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Competition Model ◽  
Interacting Species ◽  
Sufficient And Necessary Conditions ◽  
Global Positive Solution

This paper discusses the dynamics of a Gilpin–Ayala competition model of two interacting species perturbed by white noise. We obtain the existence of a unique global positive solution of the system and the solution is bounded in [Formula: see text]th moment. Then, we establish sufficient and necessary conditions for persistence and the existence of an ergodic stationary distribution of the model. We also establish sufficient conditions for extinction of the model. Moreover, numerical simulations are carried out for further support of present research.

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.

Computer Simulation for Exploring Theories: Models of Interpersonal Cooperation and Competition

1995 ◽  
Vol 38 (4) ◽  
pp. 463-482 ◽  
Author(s):  
Robert K. Leik ◽  
Barbara F. Meeker
Keyword(s):  
Computer Simulation ◽  
Competition Model ◽  
Species Competition ◽  
Minor Variation ◽  
Direct Relevance ◽  
Cooperation And Competition ◽  
Functional Forms

Computer simulation for exploring substantive theories is both powerful and convenient, but there are few standards for doing simulations. Some criteria are suggested and their importance illustrated in detail via our adaptation and augmentation of a species competition model to reflect interpersonal cooperation or competition. Outcomes of the simulation and their substantive interpretation can vary due to minor variation in parameters, to convenient functional forms assumed by the program, and to settings of function parameters which seem to have no direct relevance for the substantive interpretation of the model Under certain circumstances, chaos-like patterns emerge from the simulation.

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