# American Institute of Mathematical Sciences

2009, 12(4): 797-825. doi: 10.3934/dcdsb.2009.12.797

## Dependence of propagation speed on invader species: The effect of the predatory commensalism in two-prey, one-predator system with diffusion

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

Received  May 2008 Revised  October 2008 Published  August 2009

Biological invasion theory is one of important subjects in a biological control, an environmental preservation problem, a propagation of infectious diseases. I propose an propagation speed of traveling waves induced by an invasion of alien species for two-prey, one-predator modesl in which the commensalism induced by a predator between two prey species is considered. I investigate a spreading phenomenon and a minimal propagation speed for two cases that invader species is one species or more than one species. By numerical simulations and mathematical analysis, I conclude that the minimal speed is contingent only on the mobility of invasive species, furthermore, on that of one invader species even if two invader species invade at the same time. It is also shown that the commensalism via predator species affects spreading phenomena and a propagation speed, which is contingent on the type and the number of invasive species.
Citation: Sungrim Seirin Lee. Dependence of propagation speed on invader species: The effect of the predatory commensalism in two-prey, one-predator system with diffusion. Discrete & Continuous Dynamical Systems - B, 2009, 12 (4) : 797-825. doi: 10.3934/dcdsb.2009.12.797
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