Articles

ON THE GLOBAL STABILITY CONJECTURE OF THE GENOTYPE SELECTION MODEL

  • S.H. Saker
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  • Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received date: 2008-10-30

  Revised date: 2009-08-17

  Online published: 2011-03-20

Abstract

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.

Cite this article

S.H. Saker . ON THE GLOBAL STABILITY CONJECTURE OF THE GENOTYPE SELECTION MODEL[J]. Acta mathematica scientia, Series B, 2011 , 31(2) : 512 -528 . DOI: 10.1016/S0252-9602(11)60252-X

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