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 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 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 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. 

GLOBAL STABILITY OF A CHEMOSTAT MODEL WITH DELAYED RESPONSE IN GROWTH AND A LETHAL EXTERNAL INHIBITOR

2008 ◽  
Vol 01 (04) ◽  
pp. 503-520 ◽  
Author(s):  
ZHIQI LU ◽  
JINGJING WU
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Delayed Response ◽  
Qualitative Properties ◽  
Chemostat Model ◽  
Stability And Instability ◽  
Discrete Delays ◽  
Globally Stable

A competition model between two species with a lethal inhibitor in a chemostat is analyzed. Discrete delays are used to describe the nutrient conversion process. The proved qualitative properties of the solution are positivity, boundedness. By analyzing the local stability of equilibria, it is found that the conditions for stability and instability of the boundary equilibria are similar to those in [9]. In addition, the global asymptotic behavior of the system is discussed and the sufficient conditions for the global stability of the boundary equilibria are obtained. Moreover, by numerical simulation, it is interesting to find that the positive equilibrium may be globally stable.

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.

scholarly journals On the stability of periodic binary sequences with zone restriction

2020 ◽  
Author(s):  
Ming Su ◽  
Qiang Wang
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Linear Complexity ◽  
Binary Sequence ◽  
Search Space ◽  
Binary Sequences ◽  
Zone Length ◽  
Stability Measure ◽  
Error Linear Complexity ◽  
The Stability

Abstract Traditional global stability measure for sequences is hard to determine because of large search space. We propose the k-error linear complexity with a zone restriction for measuring the local stability of sequences. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods $$2^n$$ 2 n , or $$2^v r$$ 2 v r (r odd prime and 2 is primitive modulo r), or $$2^v p_1^{s_1} \cdots p_n^{s_n}$$ 2 v p 1 s 1 ⋯ p n s n ($$p_i$$ p i is an odd prime and 2 is primitive modulo $$p_i^2$$ p i 2 , where $$1\le i \le n$$ 1 ≤ i ≤ n ) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary $$2^n$$ 2 n -periodic binary sequence.

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