Math Bio Seminar

Bhargav Karamched
Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems


Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast-switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.

Event Date: 
September 25, 2023 - 3:30pm to 4:30pm
218 MLH or Online (See URL)
Calendar Category: 
Seminar Category: 
Mathematical Biology