Mathematical Biosciences and Engineering, 2014, 11(4): 723-740. doi: 10.3934/mbe.2014.11.723

Primary: 92D10, 34C23, 55N99; Secondary: 34F05, 57M99.

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Critical transitions in a model of a genetic regulatory system

1. Institute for Mathematics and Its Applications, Minneapolis, MN 55455
2. Yeshiva University, Department of Mathematical Sciences, New York, NY 10016

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).
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