Studying dynamical behavior of the three connected populations with Allee effect using algebraic tools

Abstract: We consider three connected populations with the strong Allee effect, and give a complete classification of the steady state structure of the system with respect to the Allee threshold and the dispersal rate. One may expect that by increasing the dispersal rate between the patches, the system would become more well-mixed hence simpler. However, we show that it is not always the case, and the number of steady states may (temporarily) increase by increasing the dispersal rate. Besides sequences of pitchfork and saddle-node bifurcations, we find triple-transcritical bifurcations and also a sun-ray shaped bifurcation where twelve steady states meet at a single point then disappear. The major tool of our investigations is a novel algorithm that decomposes the parameter space with respect to the number of steady states using cylindrical algebraic decomposition with respect to the discriminant variety of the polynomial system. This is a joint work with Gergely Röst.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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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!

The organizers.

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