Mapping dynamical systems into chemical reactions

Abstract: Polynomial dynamical systems are used to model a wide range of physical processes. A subset of these dynamical systems that can model chemical reactions under mass-action kinetics are called chemical systems. A central problem in synthetic biology is to map general polynomial dynamical systems into dynamically similar chemical ones. In this talk, I will present a novel map, called the quasi-chemical map, that can systematically solve this problem. The quasi-chemical map introduces suitable state-dependent perturbations into any given polynomial dynamical system which then becomes chemical under sufficiently large translation of variables. This map preserves robust dynamical features, such as generic equilibria and limit cycles, as well as temporal properties, such as periods of oscillations. Furthermore, the resulting chemical systems are at most one degree higher than the original dynamical systems. I will demonstrate the quasi-chemical map by designing relatively simple chemical systems with exotic dynamics and predefined bifurcations.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

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Seminar on the Mathematics of Reaction Networks

Series comments: Subscription link: list.ku.dk/postorius/lists/morn.list.ku.dk/

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.

The seminar runs twice a month, typically on the 2nd and 4th Thursday of the month, at 17:00 Brussels time (observe that this webpage shows the schedule in your current time zone). Each session consists of two 25-minute talks followed by 5-minute questions. After the two talks, longer discussions will take place for those interested. To this end, we will use breakout rooms. For this to work well, you need to have the latest version of Zoom installed (version 5.3.0 or higher), and use the desktop client or mobile app (not supported on ChromeOS).

We look forward hearing about new work and meeting many of you over zoom! Many of the talks are recorded; to see the recording, from Past Talks, open details of the listed talk for a video link.

The organizers.

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