On the dynamics of two-consumers-one-resource competing systems with Beddington-DeAngelis functional response

Sze-Bi Hsu; Shigui Ruan; Ting-Hui Yang

doi:10.3934/dcdsb.2013.18.2331

Article Contents

2013, Volume 18, Issue 9: 2331-2353. Doi: 10.3934/dcdsb.2013.18.2331

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On the dynamics of two-consumers-one-resource competing systems with Beddington-DeAngelis functional response

1.
Department of Mathematics and The National Center for Theoretical Science, National Tsing-Hua University, Hsinchu 30013
2.
Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250
3.
Department of Mathematics, Tamkang University, Tamsui, Taipei County 25137

Received: May 31, 2013

Revised: July 31, 2013

Published: October 2013

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Abstract

In this paper we study a two-consumers-one-resource competing system with Beddington-DeAngelis functional response. The two consumers competing for a renewable resource have intraspecific competition among their own populations. Firstly we investigate the extinction and uniform persistence of the predators, local and global stability of the equilibria, and existence of Hopf bifurcation at the positive equilibrium. Then we compare the dynamic behavior of the system with and without interference effects. Analytically we study the competition of two identically species with different interference effects. We also study the relaxation oscillation in the case of interference effects. Finally we present extensive numerical simulations to understand the interference effects on the competition outcomes.

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Mathematics Subject Classification: Primary: 37N25, 92D25, 92D40.

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References

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