Volume 119, Number 5, September 2017
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||28 November 2017|
Amplitude bounds for biochemical oscillators
Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge JJ Thomson Avenue, Cambridge CB3 0HE, UK and The Wellcome Trust/Cancer Research UK Gurdon Institute, University of Cambridge Tennis Court Road, Cambridge CB2 1QN, UK
Received: 31 August 2017
Accepted: 7 November 2017
We present a practical method to obtain bounds for the oscillation minima and maxima of large classes of biochemical oscillator models that generate oscillations through a negative feedback. These bounds depend on the feedback nonlinearity and are independent of explicit or effective feedback delays. For specific systems, we obtain explicit analytical expressions for the bounds and demonstrate their effectiveness in comparison with numerical simulations.
PACS: 82.39.-k – Chemical kinetics in biological systems / 87.10.Ed – Ordinary differential equations (ODE), partial differential equations (PDE), integrodifferential models / 05.45.-a – Nonlinear dynamics and chaos
© EPLA, 2017
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