期刊
MATHEMATICAL BIOSCIENCES AND ENGINEERING
卷 11, 期 4, 页码 723-740出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2014.11.723
关键词
Gene regulatory networks; critical transitions; stochastic differential equations; persistence diagrams
资金
- Mathematics and Climate Research Network through National Science Foundation [DMS-0940363]
- NSF [DMS-1201357]
- National Cancer Institute [P20 CA157069]
- Fund for Math of the IAS
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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