Persistence and global stability in a predator-prey model consisting of three prey genotypes with fertility differences |
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| Authors: | Joseph W. H. So H. I. Freedman |
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| Affiliation: | (1) Department of Mathematics and Computer Science, Emory University, 30322 Atlanta, GA, U.S.A.;(2) Department of Mathematics, University of Alberta, T6G 2G1 Edmonton, Alberta, Canada |
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| Abstract: | A model of a predator-prey interaction, where the prey population consists of three genotypes with random mating and continuous, nonlinear birth and death processes with fertility differences, is proposed. Sufficiency conditions giving the existence of a globally stable equilibrium on one of the coordinate planes are given. This extends results of Freedman and Waltman [J. Math. Biol. 6, 367–374 (1978) andRocky Mountain J. Math. 12, 779–784 (1982)]. In addition, conditions are derived which guarantee the persistence of all components of the populations. Research in part is from a Ph.D. thesis submitted to the Faculty of Graduate Studies and Research of the University of Alberta. Research partially supported by the Natural Sciences and Engineering Research Council of Canada, grant no. NSERC A4813. |
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