The non-dimensional equations for two competing populations are

$$\begin{aligned} &\frac{d u}{d t}=u(1-v)-\epsilon_{1} u^{2} \\ &\frac{d v}{d t}=\alpha\left[v(1-u)-\epsilon_{2} v^{2}\right] \end{aligned}$$

Explain the meaning of each term in these equations.

Find all the fixed points of this system when $\alpha>0,0<\epsilon_{1}<1$ and $0<\epsilon_{2}<1$, and investigate their stability.