Speaker
Description
Let's imagine "CRN space", the set of all finite chemical reaction networks (CRNs), which can be visualised as an infinite set of digraphs. We can stratify CRN space in various ways: by molecularity, by number of species or reactions, by rank, by various equivalences, and so forth. Much of CRN theory consists of theorems linking network structure and network dynamics. Many classical and modern results tell us that, under some kinetic assumptions, some dynamical behaviour is permitted or forbidden by a given set of networks. In this sense, CRN theory provides tools which bring order to CRN space. The theory of "inheritance" provides another powerful tool for this purpose: it tells us how dynamics propagates through CRN space. Its results provide partial orders on CRN space, with A <= B implying that some behaviour of network A must also occur in network B. The theory is most useful when combined with results on "atoms" - minimal networks with a given behaviour. Each atom immediately defines an upper set of networks which must have this behaviour and a lower set of networks which forbid this behaviour. I'll describe some elements of this story, and what I see as the most important missing pieces.
This talk is based on joint work with Balázs Boros (University of Szeged), Josef Hofbauer (University of Vienna), and Casian Pantea (West Virginia University).
Bibliography
@article{banaji_inheritance_2025,
title = {The inheritance of local bifurcations in mass action networks},
volume = {35},
issn = {0938-8974, 1432-1467},
url = {https://link.springer.com/10.1007/s00332-025-10165-4},
doi = {10.1007/s00332-025-10165-4},
language = {en},
number = {4},
urldate = {2026-03-10},
journal = {Journal of Nonlinear Science},
author = {Banaji, Murad and Boros, Balázs and Hofbauer, Josef},
month = aug,
year = {2025},
pages = {72},
}
@article{banaji_splitting_2023,
title = {Splitting reactions preserves nondegenerate behaviours in chemical reaction networks},
volume = {83},
issn = {0036-1399, 1095-712X},
url = {https://epubs.siam.org/doi/10.1137/22M1478392},
doi = {10.1137/22M1478392},
language = {en},
number = {2},
urldate = {2026-03-10},
journal = {SIAM Journal on Applied Mathematics},
author = {Banaji, Murad},
month = apr,
year = {2023},
pages = {748--769},
}
@article{banaji_adding_2022,
title = {Adding species to chemical reaction networks: {Preserving} rank preserves nondegenerate behaviours},
volume = {426},
issn = {00963003},
shorttitle = {Adding species to chemical reaction networks},
url = {https://linkinghub.elsevier.com/retrieve/pii/S009630032200193X},
doi = {10.1016/j.amc.2022.127109},
language = {en},
urldate = {2026-03-10},
journal = {Applied Mathematics and Computation},
author = {Banaji, Murad and Boros, Balázs and Hofbauer, Josef},
month = aug,
year = {2022},
pages = {127109},
}
@article{banaji_inheritance_2018,
title = {Inheritance of oscillation in chemical reaction networks},
volume = {325},
issn = {00963003},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0096300317308718},
doi = {10.1016/j.amc.2017.12.012},
language = {en},
urldate = {2026-03-10},
journal = {Applied Mathematics and Computation},
author = {Banaji, Murad},
month = may,
year = {2018},
pages = {191--209},
}
@article{banaji_inheritance_2018-1,
title = {The inheritance of nondegenerate multistationarity in chemical reaction networks},
volume = {78},
issn = {0036-1399, 1095-712X},
url = {https://epubs.siam.org/doi/10.1137/16M1103506},
doi = {10.1137/16M1103506},
language = {en},
number = {2},
urldate = {2026-03-10},
journal = {SIAM Journal on Applied Mathematics},
author = {Banaji, Murad and Pantea, Casian},
month = jan,
year = {2018},
pages = {1105--1130},
}
