Suppose $\dot {x}=f(x)$ is a dynamical system, $x(t,x_{0})$ is a trajectory, and $x_{0}$ is the initial point. Let $$\mathcal {O}:=\left\lbrace x\in \mathbb {R} ^{n}\mid \varphi (x)=0\right\rbrace$$ where $\varphi$ is a real-valued function. The set $\mathcal{O}$ is said to be positively invariant if $$x_{0}\in \mathcal{O} \implies x(t,x_{0})\in \mathcal{O}\ \forall \ t\geq 0.$$In other words, once a trajectory of the system enters $\mathcal {O}$, it will never leave it again.