# Critical Transitions In a Model of a Genetic Regulatory System

arXiv: https://arxiv.org/abs/1309.7919 · HTML: https://mlsanity.com/paper/1309.7919/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2013.

## Built on by (most cited first, 2 of 2)

- [Topological Neural Networks: Mitigating the Bottlenecks of Graph Neural Networks via Higher-Order Interactions](https://mlsanity.com/paper/2402.06908/) (2024)
- [Topological Detection of Hopf Bifurcations via Persistent Homology: A Functional Criterion from Time Series](https://mlsanity.com/paper/2603.27395/) (2026)

## Abstract (arXiv)

We consider a model for substrate-depletion oscillations in genetic systems, based on a stochastic differential equation with a slowly evolving external signal. We show the existence of critical transitions in the system. We apply two methods to numerically test the synthetic time series generated by the system for early indicators of critical transitions: a detrended fluctuation analysis method, and a novel method based on topological data analysis (persistence diagrams).