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Characterization of spatial topological chaos for bistable lattice equation
Abstract
In this paper we extend the description of spatial topological chaos for bistable lattice equations in a small diffusion regime. We generalize the Keener's proof and show that stationary solutions are topologically conjugate to biinfinite sequences on a three-symbol alphabet. We provide a priori estimates for the values of stationary solutions and use them to show that there are exactly two monotone stationary fronts (up to a translation). Finally, we apply the localization of all stationary solutions to characterize their stability and get the existence of unique stable and unstable monotone fronts (up to a translation).
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BibTeX
@misc{hesoun2026characterization,
title = {{Characterization of spatial topological chaos for bistable lattice equation}},
author = {Jakub Hesoun and Petr Stehlík and Jonáš Volek},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.25868},
eprint = {2609.25868},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25868},
}
RIS
TY - UNPB
TI - Characterization of spatial topological chaos for bistable lattice equation
AU - Jakub Hesoun
AU - Petr Stehlík
AU - Jonáš Volek
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2609.25868
UR - https://arxiv.org/abs/2609.25868
AB - In this paper we extend the description of spatial topological chaos for bistable lattice equations in a small diffusion regime. We generalize the Keener's proof and show that stationary solutions are topologically conjugate to biinfinite sequences on a three-symbol alphabet. We provide a priori estimates for the values of stationary solutions and use them to show that there are exactly two monotone stationary fronts (up to a translation). Finally, we apply the localization of all stationary solutions to characterize their stability and get the existence of unique stable and unstable monotone fronts (up to a translation).
ER -