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 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 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.

THE EFFECTS OF HARVESTING AND TIME DELAY ON PREDATOR-PREY SYSTEMS WITH BEDDINGTON–DEANGELIS FUNCTIONAL RESPONSE

2012 ◽  
Vol 05 (01) ◽  
pp. 1250008 ◽  
Author(s):  
XINYOU MENG ◽  
HAIFENG HUO ◽  
XIAOBING ZHANG
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Global Stability ◽  
Functional Response ◽  
Local Stability ◽  
Positive Equilibrium ◽  
Combined Effects ◽  
Predator Prey ◽  
Region Of Stability ◽  
Two Parameter

The combined effects of harvesting and time delay on predator-prey systems with Beddington–DeAngelis functional response are studied. The region of stability in model with harvesting of the predator, local stability of equilibria and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation due to the two-parameter geometric criteria developed by Ma, Feng and Lu [Discrete Contin. Dyn. Syst. Ser B9 (2008) 397–413]. The global stability of the positive equilibrium is investigated by the comparison theorem. Furthermore, local stability of steady states and the existence of Hopf bifurcation for prey harvesting are also considered. Numerical simulations are given to illustrate our theoretical findings.

scholarly journals Local Stability in 3D Discrete Dynamical Systems: Application to a Ricker Competition Model

2017 ◽  
Vol 2017 ◽  
pp. 1-16
Author(s):  
Rafael Luís ◽  
Elias Rodrigues
Keyword(s):  
Population Dynamics ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Local Stability ◽  
Three Dimensional ◽  
Discrete Dynamical Systems ◽  
Competition Model ◽  
Centre Manifold ◽  
The Stability ◽  
Centre Manifold Theorem

A survey on the conditions of local stability of fixed points of three-dimensional discrete dynamical systems or difference equations is provided. In particular, the techniques for studying the stability of nonhyperbolic fixed points via the centre manifold theorem are presented. A nonlinear model in population dynamics is studied, namely, the Ricker competition model of three species. In addition, a conjecture about the global stability of the nontrivial fixed points of the Ricker competition model is presented.

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

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

scholarly journals Light dynamics and free-to-grow standards in aspen-dominated mixedwood forests

2002 ◽  
Vol 78 (1) ◽  
pp. 137-145 ◽  
Author(s):  
Victor J Lieffers ◽  
Bradley D Pinno ◽  
Kenneth J Stadt
Keyword(s):  
Leaf Area Index ◽  
Key Words ◽  
Leaf Area ◽  
Light Transmission ◽  
Stand Density ◽  
Canopy Gaps ◽  
Light Competition ◽  
Area Index ◽  
Mixedwood Forests ◽  
Key Words Competition

This study examines light competition between aspen and spruce during the sequence of aspen development. Leaf area index and light transmission were measured or estimated for aspen stands from 2 to 125 years old. Light transmission was lowest at 15-25 years, and in some stands, transmission was less than 5% of above-canopy light. Hypothetical aspen stands with various stem configurations and heights were developed, and positions were identified that would meet or fail Alberta free-to-grow (FTG) standards. Light transmission was estimated at each position with the MIXLIGHT forest light simulator. Positions in canopy gaps or at the northern sides of canopy gaps had higher light. In general, however, there was little difference in available light between positions that met or failed FTG criteria. Stand density and size of aspen trees appears to be a better index to predict light transmission and spruce success in juvenile aspen stands than current FTG criteria. Key words: competition, free to grow, hardwood, spruce, light

Dynamical behaviors of a diffusive predator–prey model with Beddington–DeAngelis functional response and disease in the prey

2017 ◽  
Vol 10 (08) ◽  
pp. 1750119 ◽  
Author(s):  
Wensheng Yang
Keyword(s):  
Lyapunov Function ◽  
Iterative Method ◽  
Functional Response ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey Model

The dynamical behaviors of a diffusive predator–prey model with Beddington–DeAngelis functional response and disease in the prey is considered in this work. By applying the comparison principle, linearized method, Lyapunov function and iterative method, we are able to achieve sufficient conditions of the permanence, the local stability and global stability of the boundary equilibria and the positive equilibrium, respectively. Our result complements and supplements some known ones.

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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