Turing instabilities for three interacting species
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909209422987264 |
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| author | Piskovsky, Vit |
| author_facet | Piskovsky, Vit |
| contents | In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction system (ordinary differential equation) becomes an unstable homogeneous steady state of the corresponding reaction-diffusion system (partial differential equation). Similarly to a well-known inequality condition for Turing instabilities in a system with two species, I find a set of inequality conditions for a system with three species. Furthermore, I distinguish conditions for the Turing instability when spatial perturbations grow steadily and the Turing-Hopf instability when spatial perturbations grow and oscillate in time simultaneously. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14682 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Turing instabilities for three interacting species Piskovsky, Vit Pattern Formation and Solitons Dynamical Systems Spectral Theory Quantitative Methods 35B36 In this paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction system (ordinary differential equation) becomes an unstable homogeneous steady state of the corresponding reaction-diffusion system (partial differential equation). Similarly to a well-known inequality condition for Turing instabilities in a system with two species, I find a set of inequality conditions for a system with three species. Furthermore, I distinguish conditions for the Turing instability when spatial perturbations grow steadily and the Turing-Hopf instability when spatial perturbations grow and oscillate in time simultaneously. |
| title | Turing instabilities for three interacting species |
| topic | Pattern Formation and Solitons Dynamical Systems Spectral Theory Quantitative Methods 35B36 |
| url | https://arxiv.org/abs/2405.14682 |