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Published on: May 7, 2017
Traveling excitable waves successively generated in a nonlinear proliferation system
Kenta Odagiri1, Kazuo Takatsuka
1Department of Basic Science, Graduate School of Arts and Sciences, The University of Tokyo, 153-8902 Tokyo, Japan.
Summary
Spatiotemporal patterns emerge in a nonlinear proliferation system due to residual cell and activator dynamics. This cellular automata model generates traveling waves, unlike reaction-diffusion models, offering insights into pattern formation.
Area of Science:
- Nonlinear dynamics
- Pattern formation
- Cellular automata modeling
Background:
- Studying spatiotemporal pattern formation in nonlinear proliferation systems.
- Implementing simultaneous activation and self-suppression mechanisms.
Purpose of the Study:
- Investigate the dynamics of pattern formation in a nonlinear proliferation system.
- Analyze the generation of traveling waves and other spatiotemporal patterns.
- Compare the behavior of cellular automata (CA) and reaction-diffusion (RD) models.
Main Methods:
- Numerical realization using coupled cellular automata (CA).
- Analysis of a nonlinear proliferation system with simultaneous activation and self-suppression.
- Comparison between CA simulations and reaction-diffusion (RD) equation models.
Main Results:
- Observed various spatiotemporal patterns, including successive traveling waves, in the CA model.
- Identified that residual cells and activators in CA act as seeds for new wave generation.
- RD model reproduced only a single excitable wave, unlike the sustained wave generation in CA.
Conclusions:
- The CA model reveals a novel mechanism for sustained traveling wave generation in excitable systems.
- Residual dynamics in stochastic simulations are crucial for complex pattern formation.
- Pattern control is possible by manipulating initial spatial distributions of activators.
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