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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Keywords critical transitions; persistence diagrams.; Gene regulatory networks; stochastic differential equations

Citation: Jesse Berwald, Marian Gidea. Critical transitions in a model of a genetic regulatory system. Mathematical Biosciences and Engineering, 2014, 11(4): 723-740. doi: 10.3934/mbe.2014.11.723

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