Year: 2025
Type: article
Abstract: We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable reaction-diffusion equations. We show that moving traveling waves for high diffusion parameters are restricted to slow speeds, and their profiles are interestingly not unique. Pinned waves always exist for weak diffusion as in the case of lattice equations, but do not complement parametric regions of moving traveling waves. The remaining parameter domain is dominated by waves which are unique to cellular automaton settings. These higher-order traveling waves move and periodically change profile at the same time.
Authors: Daniel Špale, Petr Stehlík
Institution: University of West Bohemia in Pilsen
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7085739757