Oscillating Turing patterns, chaos and strange attractors in a reaction-diffusion system augmented with self- and cross-diffusion terms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917876388069376 |
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| author | Aymard, Benjamin |
| author_facet | Aymard, Benjamin |
| contents | In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and orbits of the latter. Special attention is paid to accuracy, a necessary condition when one wants to catch periodic orbits and to perform their linear stability analysis via Floquet multipliers. Bifurcations with respect to a single control parameter are studied in four different regimes of diffusion: linear diffusion, self-diffusion for each of the two species, and cross-diffusion. Key observations are made: development of original Turing patterns, Hopf bifurcations leading to oscillating patterns and period doubling cascades leading to chaos. Eventually, original strange attractors are reported in phase space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_17076 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Oscillating Turing patterns, chaos and strange attractors in a reaction-diffusion system augmented with self- and cross-diffusion terms Aymard, Benjamin Dynamical Systems Chaotic Dynamics In this article we introduce an original model in order to study the emergence of chaos in a reaction diffusion system in the presence of self- and cross-diffusion terms. A Fourier Spectral Method is derived to approximate equilibria and orbits of the latter. Special attention is paid to accuracy, a necessary condition when one wants to catch periodic orbits and to perform their linear stability analysis via Floquet multipliers. Bifurcations with respect to a single control parameter are studied in four different regimes of diffusion: linear diffusion, self-diffusion for each of the two species, and cross-diffusion. Key observations are made: development of original Turing patterns, Hopf bifurcations leading to oscillating patterns and period doubling cascades leading to chaos. Eventually, original strange attractors are reported in phase space. |
| title | Oscillating Turing patterns, chaos and strange attractors in a reaction-diffusion system augmented with self- and cross-diffusion terms |
| topic | Dynamical Systems Chaotic Dynamics |
| url | https://arxiv.org/abs/2412.17076 |