Trapping region

In applied mathematics, a trapping region of a dynamical system is a region such that every trajectory that starts within the trapping region will move to the region's interior and remain there as the system evolves.

More precisely, given a dynamical system with flow $$\phi_t$$ defined on the phase space $$D$$, a subset of the phase space $$N$$ is a trapping region if it is compact and $$\phi_t(N) \subset \mathrm{int}(N)$$ for all $$t > 0$$.