Discrete interaction networks: attractors and cycles

Abstract: In a discrete interaction network, species concentrations are assumed to take on a finite number of values. Interaction graphs encode the positive and negative influences between species, and can be explored for insights into the network’s dynamics. It is now well-established that in asynchronous dynamics, multistationarity is only possible in the presence of positive interaction cycles, while negative interaction cycles are linked to cyclic attractors. However, interaction graphs often contain many intertwined cycles, raising the question: which specific cycles are associated with the network's long-term behavior? How can we identify and locate them? In this talk, we will provide an overview of some answers found in the literature, as well as discuss new results and open problems.

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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