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The Power of Interstimulus Interval for the Assessment of Temporal Processing in Rodents
10:27

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Published on: April 19, 2019

Noise-induced temporal dynamics in Turing systems.

Linus J Schumacher1, Thomas E Woolley, Ruth E Baker

  • 1Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 18, 2013
PubMed
Summary
This summary is machine-generated.

Intrinsic noise can create complex dynamics in Turing patterns, like the Schnakenberg system. However, pattern switching frequencies are inconsistent, and noise alters traveling waves.

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Area of Science:

  • Chemical kinetics
  • Nonlinear dynamics
  • Pattern formation

Background:

  • Turing pattern formation systems are crucial in understanding biological and chemical self-organization.
  • Intrinsic noise is a key factor influencing the dynamics of these systems.
  • The Schnakenberg reaction-diffusion model is a well-established system for studying pattern formation.

Purpose of the Study:

  • To investigate how intrinsic noise influences temporal dynamics in Turing pattern formation.
  • To characterize the behavior of the Schnakenberg kinetics under stochastic conditions.
  • To determine if noise-induced polarity switching occurs at a defined frequency.

Main Methods:

  • Stochastic simulations were employed to model the system's behavior.
  • Power spectral methods were used for quantitative characterization.
  • Comparisons were made with analytical approximations across a wide parameter space.
  • The effect of noise on deterministically predicted traveling waves was analyzed.

Main Results:

  • Intrinsic noise can induce complex temporal dynamics and polarity switching in individual simulation runs.
  • The frequency of polarity switching was found to be inconsistent across different realizations.
  • Noise was observed to increase the amplitude of traveling waves.
  • Noise was found to decrease the speed of traveling waves.

Conclusions:

  • Intrinsic noise significantly impacts the dynamics of Turing pattern formation systems.
  • While noise can induce switching, a consistent frequency is not guaranteed.
  • Noise plays a crucial role in modifying the behavior of traveling waves, affecting their speed and amplitude.