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arXiv · 2309.15241

The toric locus of a reaction network is a smooth manifold

Gheorghe Craciun·Jiaxin Jin·Miruna-Stefana Sorea
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Abstract

We show that the toric locus of a reaction network is a smoothly embedded submanifold of the Euclidean space. More precisely, we prove that the toric locus of a reaction network is the image of an embedding and it is diffeomorphic to the product space between the affine invariant polyhedron of the network and its set of complex-balanced flux vectors. Moreover, we prove that within each affine invariant polyhedron, the complex-balanced equilibrium depends smoothly on the parameters (i.e., reaction rate constants). We also show that the complex-balanced equilibrium depends smoothly on the initial conditions.

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Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea. 2023-09-26. The toric locus of a reaction network is a smooth manifold. https://arxiv.org/abs/2309.15241

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