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

Amirhosein Sadeghimanesh (Coventry University)

Thu Apr 22, 15:30-16:00 (3 days from now)

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

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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SUMMER BREAK: We hold a summer break June-August and resume the seminar in September 2021 !

There are several workshops and conferences with minisymposia on reaction networks over the summer (online or hybrid). We are aware of the following (let us know if we are missing some):

- SIAM conference on Applied Dynamical Systems, 23-27 May 2021

- SMB 2021 (pending approval), 13-16 June 2021

- SIAM conference on Applied Algebraic Geometry (pending approval), 16-20 August 2021

Organizers: Daniele Cappelletti*, Elisenda Feliu*, Stefan Müller*
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