# Unstable Cores are the source of instability in chemical reaction networks

Source: [Unstable Cores are the source of instability in chemical reaction networks](<https://www.sota2.com/research/paper/68fa5b801e209131ce9c8fa4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:06:37.655Z

Authors: Nicola Vassena, Peter F. Stadler

Published: 2023-08-22T15:06:05.000Z

## Abstract

In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes Generalized Mass Action kinetics and Michaelis-Menten kinetics, we show that certain submatrices of the stoichiometric matrix, so-called unstable cores, are sufficient for a reaction network to admit instability and potentially give rise to such complex dynamical behavior. The determinant of the submatrix distinguishes unstable-positive feedbacks, with a single real-positive eigenvalue, and unstable-negative feedbacks without real-positive eigenvalues. Autocatalytic cores turn out to be exactly the unstable-positive feedbacks that are Metzler matrices. Thus there are sources of dynamical instability in chemical networks that are unrelated to autocatalysis. We use such intuition to design non-autocatalytic biochemical networks with superlinear growth and oscillations.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2308.11486>)

[PDF](<https://arxiv.org/pdf/2308.11486.pdf>)