Transition Dynamics in General Two-Component Reaction-Diffusion Systems
Abstract
This work provides a comprehensive characterization of the first dynamic transition of a general two-component reaction-diffusion system on a bounded interval in one spatial dimension. By rigorously addressing the difficulties arising from the non-linear interactions between the two components, this study significantly extends the scope of previous studies on dynamic transitions of reaction-diffusion systems, which focused on single-equation cases. The analysis is conducted by employing center manifold reduction within the standard classification of dynamic transition theory. A key contribution of this study is that the nonlinear terms are treated to involve arbitrary powers of the unknowns u and v. Furthermore, the theoretical framework is complemented by the analysis of a representative and simplified system. As a result of this generalization, the dynamics of a broad class of fundamental reaction-diffusion systems can be systematically classified.
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BibTeX
@misc{sengul2026transition,
title = {{Transition Dynamics in General Two-Component Reaction-Diffusion Systems}},
author = {Taylan Şengül and Burhan Tiryakioglu and Esmanur Yıldız Akıl},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38450},
eprint = {2609.38450},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38450},
}
RIS
TY - UNPB
TI - Transition Dynamics in General Two-Component Reaction-Diffusion Systems
AU - Taylan Şengül
AU - Burhan Tiryakioglu
AU - Esmanur Yıldız Akıl
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38450
UR - https://arxiv.org/abs/2609.38450
AB - This work provides a comprehensive characterization of the first dynamic transition of a general two-component reaction-diffusion system on a bounded interval in one spatial dimension. By rigorously addressing the difficulties arising from the non-linear interactions between the two components, this study significantly extends the scope of previous studies on dynamic transitions of reaction-diffusion systems, which focused on single-equation cases. The analysis is conducted by employing center manifold reduction within the standard classification of dynamic transition theory. A key contribution of this study is that the nonlinear terms are treated to involve arbitrary powers of the unknowns u and v. Furthermore, the theoretical framework is complemented by the analysis of a representative and simplified system. As a result of this generalization, the dynamics of a broad class of fundamental reaction-diffusion systems can be systematically classified.
ER -