### A two species amensalism model with non-monotonic functional response

#### Abstract

A two species amensalism model with non-monotonic functional response takes the form

$$\begin{array}{rcl}

\di\frac{dx_1}{dt}&=&x_1\Big(a_1-b_1x_1-\di\frac{c_1x_2 }{d_1+x_2^2}\Big),\\[4mm]

\di\frac{dx_2}{dt}&=&x_2(a_2-b_2x_2),

\end{array}

$$

is proposed and studied, where $a_i, b_i, i=1,2$ $c_1$ and $d_1$ are all positive constants. If $a_1b_2^2d_1+a_1a_2^2-a_2b_2c_1>0$, then the system admits a unique globally stable positive equilibrium, which means that two species could coexistent in a stable state, and if $a_1b_2^2d_1+a_1a_2^2-a_2b_2c_1<0$, then the first species will be driven to extinction, and second species will be convergence to $x_2^*=\frac{r_2}{a_{22}}$}.

**Published:**2016-10-28

**How to Cite this Article:**Runxin Wu, A two species amensalism model with non-monotonic functional response, Communications in Mathematical Biology and Neuroscience, Vol 2016 (2016), Article ID 19 Copyright © 2016 Runxin Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

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