Classification of constrained differential equations embedded in the theory of slow fast systems: Ak singularities and geometric desingularization

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Abstract

Many natural phenomena take place at different time scales. Think of the heartbeat, nerve activity, chemical reactions or the weather. Such phenomena can therefore be modeled by so-called "slow-fast" systems. These are ordinary differential equations that depend singularly on a small parameter. When this parameter is set to zero, a differential equation with an algebraic constraint arises.

The Groningen mathematician Floris Takens (1940-2010) made major contributions in 1975 to the theory of differential equations with algebraic constraints and their relationship to slow-fast systems. His results are particularly useful if one wants to study the more complicated dynamics of slow-fast systems.

This thesis is a study of the dynamics and local properties of slow-fast systems and the related differential equations with algebraic constraints. The main result of this research is an extension of the results of Takens in relation to the classification of differential equations with algebraic constraints. Based on this extension, we have developed a unified method to study the dynamics of a large class of slow-fast systems.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • University of Groningen
Supervisors/Advisors
  • Broer, Henk, Supervisor
  • Vegter, Gert, Supervisor
Award date12-Jun-2015
Place of Publication[Groningen]
Publisher
Print ISBNs978-90-367-7868-8
Publication statusPublished - 2015

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