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 ${\displaystyle \phi _{t}}$ defined on the phase space ${\displaystyle D}$, a subset of the phase space ${\displaystyle N}$ is a trapping region if it is compact and ${\displaystyle \phi _{t}(N)\subset \mathrm {int} (N)}$ for all ${\displaystyle t>0}$.^[1]