Using Bogdanov-Takens bifurcations to study existence and stability of periodic solutions

Alan Rendall (Johannes Gutenberg University Mainz)

08-Apr-2021, 15:30-16:00 (3 years ago)

Abstract: Hopf bifurcations are a favourite way to prove the existence of periodic solutions of a dynamical system. The aim of this talk is to describe a variant of this procedure using the less familiar concept of a Bogdanov-Takens bifurcation. Surprisingly, the latter procedure has the advantage that although the bifurcation itself is more complicated the conditions which need to be checked to determine the stability of the periodic solutions produced are more straightforward. I will give a general discussion of these matters, illustrating them by the example of a model for the kinase Lck. This is based on work with Lisa Kreusser, where we studied the occurrence of interesting dynamical features, such as multistability, periodic solutions and homoclinic loops, in models for enzymes subject to autophosphorylation. I will also discuss how features of this type can be lifted from smaller to larger reaction networks.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )


Seminar on the Mathematics of Reaction Networks

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This seminar series focuses on progress in mathematical theory for the study of reaction networks, mainly in biology and chemistry. The scope is broad and accommodates works arising from dynamical systems, stochastics, algebra, topology and beyond.

We aim at providing a common forum for sharing knowledge and encouraging discussion across subfields. In particular we aim at facilitating interactions between junior and established researchers. These considerations will be represented in the choice of invited speakers and we will strive to create an excellent, exciting and diverse schedule.

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The organizers.

Organizers: Daniele Cappelletti*, Stefan Müller*, Tung Nguyen*, Polly Yu*
*contact for this listing

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