Speaker
Description
Memory and delay naturally arise in mathematical models across physical scales. In molecular simulations, the generalized Langevin equation is a stochastic integro-differential equation describing a molecule (or a degree of freedom) subjected to colored (time-correlated) noise and a non-Markovian friction term~\cite{ref2,ref4}. In chemotaxis, cells respond to extracellular signals through intracellular signal transduction networks, and this internal dynamics naturally introduces delays and `chemical memory' in signal processing~\cite{ref1,ref4}. In collective animal behaviour, systems of interacting individuals base their observations and responses to stimuli not only on their present state but also on the system’s past history, with models accounting for transmission delays and reaction delays to signals~\cite{ref3,ref4}. In this talk, I will discuss how the parameters of delay equations relate to those of more detailed, non-delayed models and how population-level properties can be established for mathematical biology systems described by coupled delay equations.
Bibliography
@article{ref1,
title={Neural networks for learning macroscopic chemotactic sensitivity from microscopic models},
author={Erban, R.},
journal={SIAM Journal on Life Sciences},
note={arXiv preprint arXiv:2509.12131},
year={2026}
}
@article{ref2,
author = {Erban, R.},
title = "Coarse-graining molecular dynamics: stochastic models with non-{G}aussian force distributions",
journal = {Journal of Mathematical Biology},
volume = 80,
pages = {457-479},
year = {2020}
}
@article{ref3,
title={Impact of memory on clustering in spontaneous particle aggregation},
author={Erban, R. and Haskovec, J.},
journal={SIAM Journal on Life Sciences},
note={arXiv preprint arXiv:2510.15335},
year={2026}
}
@book{ref4,
title={Stochastic {M}odelling of {R}eaction-{D}iffusion {P}rocesses},
author={Erban, R. and Chapman, S. J.},
ISBN = {9781108498128},
doi = {10.1017/9781108628389},
year={2020},
publisher={Cambridge University Press}
}
