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 [math]\displaystyle{ \phi_t }[/math] defined on the phase space [math]\displaystyle{ D }[/math], a subset of the phase space [math]\displaystyle{ N }[/math] is a trapping region if it is compact and [math]\displaystyle{ \phi_t(N) \subset \mathrm{int}(N) }[/math] for all [math]\displaystyle{ t \gt 0 }[/math].