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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. |
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| | More precisely, given a [[dynamical system]] with [[flow (mathematics)|flow]] <math>\phi_t</math> defined on the phase space <math>D</math>, a subset of the phase space <math>N</math> is a trapping region if it is [[compact space|compact]] and <math>\phi_t(N) \subset \mathrm{int}(N)</math> for all <math>t > 0</math>.<ref>Meiss, J. D., ''Differential dynamical systems'', Philadelphia: Society for Industrial and Applied Mathematics, 2007.</ref> |
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| | ==References== |
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| | {{Systems}} |
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| | {{DEFAULTSORT:Trapping region}} |
| | [[Category:Dynamical systems| ]] |
| | [[Category:Systems theory]] |
| | [[Category:Systems]] |
Revision as of 13:47, 28 July 2013
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 defined on the phase space , a subset of the phase space is a trapping region if it is compact and for all .[1]
References
- ↑ Meiss, J. D., Differential dynamical systems, Philadelphia: Society for Industrial and Applied Mathematics, 2007.
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