Abstract:
The ecological notion of system persistence in modeling the interaction of two competing predatory populations living exclusively on a common prey, is investigated. Freedom and Waltman [3], and El-Owaidy and Ammar [4] have discussed the persistence of such models based upon the assumption of nonexistence of limit cycles. In this paper, however; the nonexistence of limit cycles is proven, first, by global asymptotic stability of equilibria through the constriction of a suitable Lyapunov function, and second, persistence criteria of the system are obtained.
Page(s):
47-53
DOI:
DOI not available
Published:
Journal: Punjab University Journal of Mathematics, Volume: 39, Issue: 0, Year: 2007