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 socalled "slowfast" 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 (19402010) made major contributions in 1975 to the theory of differential equations with algebraic constraints and their relationship to slowfast systems. His results are particularly useful if one wants to study the more complicated dynamics of slowfast systems.
This thesis is a study of the dynamics and local properties of slowfast 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 slowfast systems.
The Groningen mathematician Floris Takens (19402010) made major contributions in 1975 to the theory of differential equations with algebraic constraints and their relationship to slowfast systems. His results are particularly useful if one wants to study the more complicated dynamics of slowfast systems.
This thesis is a study of the dynamics and local properties of slowfast 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 slowfast systems.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  12Jun2015 
Place of Publication  [Groningen] 
Publisher  
Print ISBNs  9789036778688 
Publication status  Published  2015 