An Iterative Method for the Approximation of Fibers in Slow-Fast Systems

作者：Kristiansen K Uldall^*; Brons M; Starke J

来源：SIAM Journal on Applied Dynamical Systems, 2014, 13(2): 861-900.

DOI：10.1137/120889666

• slow-fast systems
• singular perturbation theory
• reduction methods

In this paper we extend a method for iteratively improving slow manifolds so that it also can be used to approximate the fiber directions. The extended method is applied to general finite-dimensional real analytic systems where we obtain exponential estimates of the tangent spaces to the fibers. The method is demonstrated on the Michaelis-Menten-Henri model and the Lindemann mechanism. The latter example also serves to demonstrate the method on a slow-fast system in nonstandard slow-fast form. Finally, we extend the method further so that it also approximates the curvature of the fibers.

• 出版日期2014