ON THE GLOBAL STABILITY CONJECTURE OF THE GENOTYPE SELECTION MODEL

ON THE GLOBAL STABILITY CONJECTURE OF THE GENOTYPE SELECTION MODEL

In 1994, Grove, Kocic, Ladas, and Levin conjectured that the local stability and global stability conditions of the fixed point -y= 1/2 in the genotype selection model should be equivalent. In this article, we give an affirmative answer to this conjecture and prove that local stability implies globa...

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Veröffentlicht in:Acta mathematica scientia 2011-03, Vol.31 (2), p.512-528
1. Verfasser: Saker, S.H.
Format: Artikel
Sprache:eng
Schlagworte:
39A12
92D25
discrete genotype selection model
global stability
Local stability
全局稳定性
固定点
基因型
基因选择模型
局部稳定性
适用性
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Beschreibung
Zusammenfassung:In 1994, Grove, Kocic, Ladas, and Levin conjectured that the local stability and global stability conditions of the fixed point -y= 1/2 in the genotype selection model should be equivalent. In this article, we give an affirmative answer to this conjecture and prove that local stability implies global stability. Some illustrative examples are included to demonstrate the validity and applicability of the results.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(11)60252-X