Consider a continuous-time dynamical system defined by $$ \dot{x}=f(x), \quad x \in \mathbb{R}^{n}, $$ where $f$ is sufficiently smooth, $f(0)=0$.
Is is possible to determine the existence of a trapping region when $n>2$? I am not asking for the general behavior of an orbit inside the potential trapping region (whether it goes to a fixed point, goes to a limit cycle or neither) I am asking what would be the criteria for a trapping region to exist?