Ultradiscretization of reaction-diffusion type partial differential equations exhibiting pulse propagation
https://doi.org/10.17586/2220-8054-2017-8-1-38-41
Abstract
Cellular automaton rules are derived from a set of reaction-diffusion partial differential equations by means of ultradiscretization method. The rulesres produce dynamical properties of pulse: annihilation, soliton-like preservation and periodic generation with a pacemaker.
Keywords
ultradiscretization,
tropicaldiscretization,
pulsedynamics,
cellularautomaton,
reaction-diffusion systems
Supporting agencies: The authors are grateful to Professor Daisuke Takahashi, Professor Tomoyuki Yamamoto, and Emeritus Pro fessor Akihiko Kitada for useful discussions and encouragement.
About the Authors
Y. Yamazaki
DepartmentofPhysics,DepartmentofPhysics,SchoolofAdvancedScienceandEngineering
Japan
Japan
WasedaUniversity,Shinjuku,Tokyo169-8555
S. Ohmori
DepartmentofPhysics,DepartmentofPhysics,SchoolofAdvancedScienceandEngineering
Japan
Japan
WasedaUniversity,Shinjuku,Tokyo169-8555
Review
For citations:
Yamazaki Y., Ohmori S. Ultradiscretization of reaction-diffusion type partial differential equations exhibiting pulse propagation. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(1):38–41. https://doi.org/10.17586/2220-8054-2017-8-1-38-41
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