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 ϕ t {\displaystyle \phi _{t}} defined on the phase space D {\displaystyle D} , a subset of the phase space N {\displaystyle N} is a trapping region if it is compact and ϕ t ( N ) ⊂ i n t ( N ) {\displaystyle \phi _{t}(N)\subset \mathrm {int} (N)} for all t > 0 {\displaystyle t>0} .
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