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Coloured Noise from Stochastic Inflows in Reaction-Diffusion Systems.

Michael F Adamer1, Heather A Harrington2, Eamonn A Gaffney2

  • 1Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, UK. mikeadamer@gmail.com.

Bulletin of Mathematical Biology
|March 22, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a framework for analyzing colored noise in reaction-diffusion systems. It shows how parameter fluctuations create colored noise and how power spectra predict system behavior.

Keywords:
Chemical reaction networksColoured noiseInjectivity criterionPower spectraReaction–diffusion

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Area of Science:

  • Chemical kinetics
  • Non-linear dynamics
  • Computational modeling

Background:

  • Reaction-diffusion systems are fundamental in modeling spatial patterns.
  • Understanding noise effects is crucial for accurate system prediction.
  • Deterministic models often fail to capture stochastic phenomena.

Purpose of the Study:

  • To develop a framework for investigating colored noise in reaction-diffusion systems.
  • To analyze how external forcing and parameter fluctuations induce colored noise.
  • To connect algebraic analysis with stochastic modeling for reaction systems.

Main Methods:

  • Analysis of deterministic reaction-diffusion equations with external forcing.
  • Application of real algebraic geometry to link network structure and dynamics.
  • Utilizing parameter-free approaches for steady-state analysis.
  • Employing power spectral methods for internal noise models.

Main Results:

  • Demonstrated that parameter fluctuations in reaction systems can generate temporally correlated (colored) noise.
  • Identified reaction systems admitting a single steady state to simplify analysis.
  • Established a connection between internal noise models and external noise sources.
  • Showed that power spectra of colored noise and white noise models can predict system behavior.

Conclusions:

  • The proposed framework effectively analyzes colored noise in reaction-diffusion systems.
  • Power spectral methods offer a predictive tool for stochastic patterns in such systems.
  • The study bridges algebraic and stochastic approaches in chemical reaction network theory.