Extending the zero-derivative principle for slow–fast dynamical systems

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• 作者：Eric Beno?t ; Morten Br?ns ; Mathieu Desroches…
• 关键词：34D15 ; 37D10 ; Slow–fast dynamics ; Zero ; derivative principle ; Slow manifolds ; Fenichel theory ; Curvature ; Intrinsic low ; dimensional manifolds ; Ghosts ; Templator
• 刊名：Zeitschrift f篓鹿r angewandte Mathematik und Physik
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：66
• 期：5
• 页码：2255-2270
• 全文大小：1,184 KB
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• 作者单位：Eric Beno?t (1)
  Morten Br?ns (2)
  Mathieu Desroches (3)
  Martin Krupa (4)
  
  1. Laboratoire Mathématiques Images et Applications, Université de la Rochelle, EA3165 Avenue Michel Crépeau, 17042, La Rochelle Cedex, France
  2. Department of Applied Mathematics and Computer Science, Technical University of Denmark, 2800, Kongens Lyngby, Denmark
  3. Project-Team MYCENAE, Inria Paris-Rocquencourt Research Centre, Domaine de Voluceau, BP 105, 78153, Le Chesnay Cedex, France
  4. Project-Team NEUROMATHCOMP, Inria Sophia Antipolis Méditerranée, 2004 Route des Lucioles, BP 93, 06902, Valbonne, France
  
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer Basel
• ISSN：1420-9039

文摘

Slow–fast systems often possess slow manifolds, that is invariant or locally invariant sub-manifolds on which the dynamics evolves on the slow time scale. For systems with explicit timescale separation, the existence of slow manifolds is due to Fenichel theory, and asymptotic expansions of such manifolds are easily obtained. In this paper, we discuss methods of approximating slow manifolds using the so-called zero-derivative principle. We demonstrate several test functions that work for systems with explicit time scale separation including ones that can be generalized to systems without explicit timescale separation. We also discuss the possible spurious solutions, known as ghosts, as well as treat the Templator system as an example. Mathematics Subject Classification 34D15 37D10