Intrinsic low-dimensional manifold

In chemical kinetics, an intrinsic low-dimensional manifold is a technique to simplify the study of reaction mechanisms using dynamical systems, first proposed in 1992.{{Cite journal | doi = 10.1016/S0082-0784(06)80017-2| title = Implementation of simplified chemical kinetics based on intrinsic low-dimensional manifolds| journal = Symposium (International) on Combustion| volume = 24| pages = 103–112| year = 1992| last1 = Maas | first1 = U.| last2 = Pope | first2 = S. B. | url = https://tcg.mae.cornell.edu/pubs/Maas_P_PCI_92.pdf}}{{Cite journal | doi = 10.1016/0010-2180(92)90034-M| title = Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space| journal = Combustion and Flame| volume = 88| issue = 3–4| pages = 239| year = 1992| last1 = Maas | first1 = U.| last2 = Pope | first2 = S. B. | url = https://tcg.mae.cornell.edu/pubs/Maas_P_CF_92.pdf}}{{Cite journal | doi = 10.1016/S1540-7489(02)80168-7| title = Intrinsic low-dimensional manifold method extended with diffusion| journal = Proceedings of the Combustion Institute| volume = 29| pages = 1371–1378| year = 2002| last1 = Bongers | first1 = H.| last2 = Van Oijen | first2 = J. A. | last3 = De Goey | first3 = L. P. H. }}

The ILDM approach fixes a low dimensional surface which describes well the slow dynamics and assumes that after a short time the fast dynamics are less important and the system can be described in the lower-dimensional space.{{Cite book | doi = 10.1007/978-3-662-04956-3_25| chapter = The Estimation of Intrinsic Low Dimensional Manifold Dimension in Atmospheric Chemical Reaction Systems| title = Air Pollution Modelling and Simulation| pages = 245| year = 2002| last1 = Tomlin | first1 = A. S. |author1-link=Alison Tomlin| last2 = Whitehouse | first2 = L. | last3 = Lowe | first3 = R. | isbn = 978-3-642-07637-4}}