Acta mathematica scientia,Series B ›› 2011, Vol. 31 ›› Issue (2): 512-528.doi: 10.1016/S0252-9602(11)60252-X

• Articles • Previous Articles     Next Articles

ON THE GLOBAL STABILITY CONJECTURE OF THE GENOTYPE SELECTION MODEL

S.H. Saker   

  1. Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
  • Received:2008-10-30 Revised:2009-08-17 Online:2011-03-20 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.

Key words: Local stability, global stability, discrete genotype selection model

CLC Number: 

  • 39A12
Trendmd