Persistence in predator-prey systems with ratio-dependent predator influence |
| |
Authors: | H. I. Freedman R. M. Mathsen |
| |
Affiliation: | (1) Department of Mathematics, Applied Mathematics Institute, University of Alberta, T6G 2G1 Edmonton, Alberta, Canada;(2) Department of Mathematics, North Dakota State University, 58105-5057 Fargo, ND, U.S.A. |
| |
Abstract: | Predator-prey models where one or more terms involve ratios of the predator and prey populations may not be valid mathematically unless it can be shown that solutions with positive initial conditions never get arbitrarily close to the axis in question, i.e. that persistence holds. By means of a transformation of variables, criteria for persistence are derived for two classes of such models, thereby leading to their validity. Although local extinction certainly is a common occurrence in nature, it cannot be modeled by systems which are ratio-dependent near the axes. Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A4823. Research carried out while visiting the University of Alberta. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|