The structure of the moduli spaces of toric dynamical systems
Abstract
We consider complex-balanced mass-action systems, or toric dynamical systems. They are remarkably stable polynomial dynamical systems arising from reaction networks seen as Euclidean embedded graphs. We study the moduli spaces of toric dynamical systems, called the toric locus: given a reaction network, we are interested in the topological structure of the set of parameters giving rise to toric dynamical systems. First we show that the complex-balanced equilibria depend continuously on the parameter values. Using this result, we prove that the toric locus of any toric dynamical system is connected. In particular, we emphasize its product structure: it is homeomorphic to the product of the set of complex-balanced flux vectors and the affine invariant polyhedron. Finally, we show that the toric locus is invariant with respect to bijective affine transformations of the generating reaction network.
Keywords
Cite
@article{arxiv.2303.18102,
title = {The structure of the moduli spaces of toric dynamical systems},
author = {Gheorghe Craciun and Jiaxin Jin and Miruna-Stefana Sorea},
journal= {arXiv preprint arXiv:2303.18102},
year = {2023}
}
Comments
We intended to upload arXiv:2303.18102 [v1] as a second version of arXiv:2008.11468 [v1]. Instead, we uploaded arXiv:2303.18102 [v1] unintentionally as a new arXiv submission. We withdraw the version arXiv:2303.18102 [v1] and we will submit the content of arXiv:2303.18102 [v1] (with a few more updates) as version [v2] for arXiv:2008.11468 [v1]. Please follow arXiv:2008.11468 for future updates