Cellular automaton obtained by the tropical discretization from the competitive diffusion equation
Author:
Affiliation:
1. Institute of Engineering, Tokyo University of Agriculture and Technology
Publisher
The Japan Society for Industrial and Applied Mathematics
Subject
General Engineering
Link
https://www.jstage.jst.go.jp/article/jsiaml/14/0/14_61/_pdf
Reference7 articles.
1. 1) M. Murata, Tropical discretization: ultradiscrete Fisher-KPP equation and ultradiscrete Allen-Cahn equation, J. Differ. Equ. Appl., 19 (2013), 1008-1021.
2. 2) M. Murata, Multidimensional traveling waves in Allen-Cahn cellular automaton, J. Phys. A: Math. Theor., 48 (2015), 255202.
3. 3) K. Matsuya and M. Murata, Spatial pattern of discrete and ultradiscrete Gray-Scott model, Discrete Contin. Dyn. Syst. Ser. B, 20 (2015), 173-187.
4. 4) R. A. Gardner, Existence and stability of travelling wave solutions of competition models: A degree theoretic approach, J. Differ. Equ., 44 (1982), 343-364.
5. 5) C. Conley and R. Gardner, An application of the generalized Morse index to travelling wave solutions of a competitive reaction-diffusion model, Indiana Univ. Math. J., 33 (1984), 319-343.
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