Critical transitions in a model of a genetic regulatory system

  • 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

    Related Papers:

  • 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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