`a`
Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Intraspecific interference and consumer-resource dynamics

Pages: 527 - 546, Volume 4, Issue 3, August 2004      doi:10.3934/dcdsb.2004.4.527

 
       Abstract        Full Text (308.2K)       Related Articles

Robert Stephen Cantrell - Department of Mathematics, University of Miami, P. O . Box 249085, Coral Gables, FL 33124-4250, United States (email)
Chris Cosner - Department of Mathematics, University of Miami, P. O . Box 249085, Coral Gables, FL 33124-4250, United States (email)
Shigui Ruan - Department of Mathematics, The University of Miami, P.O. Box 249085, Coral Gables, Florida 33124, United States (email)

Abstract: 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:  Predators interference, competition, coexistence, persistence, stability.
Mathematics Subject Classification:  34D20, 92D25.

Received: February 2003;      Revised: January 2004;      Available Online: May 2004.