Rigorous integration of smooth vector fields around spiral saddles with an application to the cubic Chua's attractor

Zbigniew Galias, Warwick Tucker

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2 Citations (Scopus)

Abstract

In this paper, we present a general mathematical framework for integrating smooth vector fields in the vicinity of a fixed point with a spiral saddle. We restrict our study to the three-dimensional setting, where the stable manifold is of spiral type (and thus two-dimensional), and the unstable manifold is one-dimensional. The aim is to produce a general purpose set of bounds that can be applied to any system of this type. The existence (and explicit computation) of such bounds is important when integrating along the flow near the spiral saddle fixed point. As an application, we apply our work to a concrete situation: the cubic Chua's equations. Here, we present a computer assisted proof of the existence of a trapping region for the flow.

Original languageEnglish
Pages (from-to)2408-2434
Number of pages27
JournalJournal of Differential Equations
Volume266
Issue number5
DOIs
Publication statusPublished - 15 Feb 2019
Externally publishedYes

Keywords

  • Differential equations
  • Normal forms
  • Rigorous computations

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