Statistical pulse dynamics in a reaction–diffusion system . Ohta, T. & Yoshimura, T. Physica D: Nonlinear Phenomena , 205(1–4):189 - 194, 2005. Synchronization and Pattern Formation in Nonlinear Systems: New Developments and Future PerspectivesA Special Issue dedicated to Professor Yushiki Kuramoto
Statistical pulse dynamics in a reaction–diffusion system  [link]Paper  doi  abstract   bibtex   
We study a nonlinear response to random external stimuli in an excitable reaction–diffusion system. Numerical simulations are carried out in one dimension to investigate formation of excited domains (pulses) in response to stimuli and pair-annihilate upon collision. Our main concern is how the area of excited domains in the steady state depends on the strength of stimuli. We have found three different stimuli-response behaviors: a power law dependence for sufficiently weak stimuli, a logarithmic dependence for intermediate strength and an oscillatory behavior for strong stimuli. The power law behavior can be understood by a theoretical analysis.
@article{Ohta2005189,
title = "Statistical pulse dynamics in a reaction–diffusion system ",
journal = "Physica D: Nonlinear Phenomena ",
volume = "205",
number = "1–4",
pages = "189 - 194",
year = "2005",
note = "Synchronization and Pattern Formation in Nonlinear Systems: New Developments and Future PerspectivesA Special Issue dedicated to Professor Yushiki Kuramoto ",
issn = "0167-2789",
doi = "http://dx.doi.org/10.1016/j.physd.2005.01.023",
url = "http://www.sciencedirect.com/science/article/pii/S0167278905000722",
author = "T. Ohta and T. Yoshimura",
keywords = "Pulse dynamics",
keywords = "Excitability",
keywords = "Stimuli-response relation",
keywords = "Reaction–diffusion systems ",
abstract = "We study a nonlinear response to random external stimuli in an excitable reaction–diffusion system. Numerical simulations are carried out in one dimension to investigate formation of excited domains (pulses) in response to stimuli and pair-annihilate upon collision. Our main concern is how the area of excited domains in the steady state depends on the strength of stimuli. We have found three different stimuli-response behaviors: a power law dependence for sufficiently weak stimuli, a logarithmic dependence for intermediate strength and an oscillatory behavior for strong stimuli. The power law behavior can be understood by a theoretical analysis. "
}
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