Invariant Manifolds of Complex Systems
Dynamical Systems
2014-08-19 v1
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.
Cite
@article{arxiv.1408.3916,
title = {Invariant Manifolds of Complex Systems},
author = {Jean-Marc Ginoux and Bruno Rossetto},
journal= {arXiv preprint arXiv:1408.3916},
year = {2014}
}
Comments
arXiv admin note: text overlap with arXiv:1408.1711