Reaction network operations that double the steady-state capacity

Abstract: A great deal of recent research has focused on proving that certain operations on reaction networks preserve dynamical properties of interest in applications. One such property is the capability for multistationarity (multiple steady states). However, little is known about how high the number of steady states can increase after such an operation. Here we construct operations that, under certain conditions, double a network's steady-state capacity (the maximum number of positive steady states). These operations typically introduce one new species and several new reactions.

Moreover, we establish sufficient conditions for these operations to increase the number of stable steady states. This allows for the possibility of turning a monostable (one stable steady state) network into a multistable (multiple stable steady states) one. The operations can also be tuned to control the locations of the new stable steady states; in particular it is possible to create new stable steady states near the location of unstable steady states in the old system.

A joint work with Badal Joshi, Nidhi Kaihnsa and Anne Shiu.

algebraic geometrydynamical systemsprobability

Audience: researchers in the topic

( video )

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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.

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).

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