American Institute of Mathematical Sciences

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August  2004, 4(3): 527-546. doi: 10.3934/dcdsb.2004.4.527

Intraspecific interference and consumer-resource dynamics

Robert Stephen Cantrell 1, , Chris Cosner 1, and  Shigui Ruan 2,

1. 

Department of Mathematics, University of Miami, P. O . Box 249085, Coral Gables, FL 33124-4250, United States, United States
2. 

Department of Mathematics, The University of Miami, P.O. Box 249085, Coral Gables, Florida 33124

Received  February 2003 Revised  January 2004 Published  May 2004

In this paper we first consider a two consumer-one resource model with one of the consumer species exhibits intraspecific feeding interference but there is no interspecific competition between the two consumer species. We assume that one consumer species exhibits Holling II functional response while the other consumer species exhibits Beddington-DeAngelis functional response. Using dynamical systems theory, it is shown that the two consumer species can coexist upon the single limiting resource in the sense of uniform persistence. Moreover, by constructing a Liapunov function it is shown that the system has a globally stable positive equilibrium. Second, we consider a model with an arbitrary number of consumers and one single limiting resource. By employing practical persistence techniques, it is shown that multiple consumer species can coexist upon a single resource as long as all consumers exhibit sufficiently strong conspecific interference, that is, each of them exhibits Beddington-DeAngelis functional response.
Keywords: coexistence, competition, stability., Predators interference, persistence.
Mathematics Subject Classification: 34D20, 92D2.
Citation: Robert Stephen Cantrell, Chris Cosner, Shigui Ruan. Intraspecific interference and consumer-resource dynamics. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 527-546. doi: 10.3934/dcdsb.2004.4.527
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