Survival and extinction in competitive systems

✍ Scribed by Shair Ahmad; Ivanka Stamova

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 171 KB
• Volume: 9
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2006.12.011

✦ Synopsis

In [S. Ahmad, I.M. Stamova, Almost necessary and sufficient conditions for survival of species, Nonlinear Anal. Real World Appl. 5 ( 2004)], implications of various inequalities involving interaction coefficients and averages of the growth rates were listed for a two-dimensional Lotka-Volterra system, and it was shown that the first condition can be extended to one that is almost necessary and sufficient for persistence of a three-dimensional Lotka-Volterra system. In this paper, we give similar extensions of all the cases. We also explore the relationship of the (I, J ) condition, a notion defined by Ahmad-Lazer recently (see [S. Ahmad, A.C. Lazer, Average growth and total permanence in a competitive Lotka-Volterra system, Ann. Mat. 185 (2006)]), to certain known conditions which imply persistence.