1 (2.4) has no interior steady state and $$E_{0}$$ is GAS in $$\mathbb {R}_{+}^{2}$$.
2 (2.4) has a unique interior steady state $$E^{*}$$ which is GAS in Γ.
3 (2.4) has a unique interior steady state $$E^{*}$$ which is non-hyperbolic. $$W^{s}$$ separates $$\mathbb{R}_{+}^{2}$$ into two positively invariant regions $$R_{1}$$ and $$R_{2}$$ such that $$E_{0}$$ is GAS in $$R_{2}$$ and solutions with initial conditions in $$R_{1}$$ converge to $$E^{*}$$.
4 (2.4) has two hyperbolic interior steady states $$E_{1}^{*}$$ and $$E_{2}^{*}$$. $$W_{2}^{s}$$ separates $$\mathbb{R}_{+}^{2}$$ into two positively invariant regions $$R_{1}$$ and $$R_{2}$$ such that $$E_{1}^{*}$$ and $$E_{0}$$ are GAS in $$R_{1}$$ and $$R_{2}$$, respectively.
5 (2.4) has two interior steady states, one is hyperbolic and the other is non-hyperbolic. The global stable manifold of the non-hyperbolic steady state separates $$\mathbb{R}_{+}^{2}$$ into two positively invariant regions $$R_{1}$$ and $$R_{2}$$ such that the other interior steady state is GAS in $$R_{1}$$ and $$E_{0}$$ is GAS in $$R_{2}$$.
6 (2.4) has three interior steady states $$E_{i}^{*}$$, i = 1,2,3. $$W_{2}^{s}$$ separates $$\mathbb{R}_{+}^{2}$$ into two positively invariant regions $$R_{1}$$ and $$R_{2}$$ such that $$E_{1}^{*}$$ and $$E_{3}^{*}$$ are GAS in $$R_{1}$$ and $$R_{2}$$, respectively.