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March  2008, 9(2): 353-374. doi: 10.3934/dcdsb.2008.9.353

The effect of the remains of the carcass in a two-prey, one-predator model

Sungrim Seirin Lee 1, and  Tsuyoshi Kajiwara 2,

1. 

Graduate School of Environmental Science, Okayama University, Tsushimanaka 3-1-1, Okayama, 700-8530, Japan
2. 

Graduate School of Environmental and Life Science, Okayama University, Tsushimanaka 3-1-1, Okayama, 700-8530, Japan

Received  May 2007 Revised  October 2007 Published  December 2007

We propose a two-prey, one-predator model involving the effect of the carcass. We consider a commensal interaction that a prey species eats the remains of the other prey species’ carcass given by their predator. Under some biological assumptions, we construct two ODE models. We analyze the linear stability and prove the permanence of the two models. We also show that the effect of the remains of the carcass leads to chaotic dynamics for biologically reasonable choices of parameters by numerical simulations. Finally, we discuss the dynamical results and the coexistent regions of the three species.
Keywords: population dynamics, Mathematical modeling, chaos..
Mathematics Subject Classification: Primary: 93A30, 92D25; Secondary: 65P2.
Citation: Sungrim Seirin Lee, Tsuyoshi Kajiwara. The effect of the remains of the carcass in a two-prey, one-predator model. Discrete and Continuous Dynamical Systems - B, 2008, 9 (2) : 353-374. doi: 10.3934/dcdsb.2008.9.353
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