Skip to Main content Skip to Navigation
Book sections

Invariant Manifolds of Complex Systems

Abstract : The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal bursting models) it is shown that there exists in the phase space a curve (resp. a surface) which is invariant with respect to the flow of such systems. These invariant manifolds are playing a very important role in the stability of complex systems in the sense that they are "restoring" the determinism of trajectory curves.
Document type :
Book sections
Complete list of metadata

Cited literature [6 references]  Display  Hide  Download
Contributor : Jean-Marc Ginoux Connect in order to contact the contributor
Submitted on : Monday, August 18, 2014 - 8:02:29 AM
Last modification on : Thursday, February 7, 2019 - 4:13:37 PM
Long-term archiving on: : Tuesday, April 11, 2017 - 8:09:31 PM


Files produced by the author(s)




Jean-Marc Ginoux, Bruno Rossetto. Invariant Manifolds of Complex Systems. Cyrille Bertelle, Gérard H.E. Duchamp, Hakima Kadri-Dahmani. Complex Systems and Self-organization Modelling, Understanding Complex System, Springer Berlin Heidelberg, pp.41-49, 2009, Understanding Complex Systems, 978-3-540-88072-1. ⟨10.1007/978-3-540-88073-8_4⟩. ⟨hal-01056170v2⟩



Record views


Files downloads