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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 ${\displaystyle t>0}$.

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