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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 4: 723-740. doi: 10.3934/mbe.2014.11.723
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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
  • Received: 01 January 2013 Accepted: 29 June 2018 Published: 01 March 2014

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

  • 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).

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

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  • 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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