rd-spiral: An open-source Python library for learning 2D reaction-diffusion dynamics through pseudo-spectral method
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912449908703232 |
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| author | Herho, Sandy H. S. Anwar, Iwan P. Suwarman, Rusmawan |
| author_facet | Herho, Sandy H. S. Anwar, Iwan P. Suwarman, Rusmawan |
| contents | We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis $>96$) in stable states. Information-theoretic metrics show $10.7\%$ reduction in activator-inhibitor coupling during turbulence versus $6.5\%$ in stable regimes. The solver handles stiffness ratios $>6:1$ with features including automated equilibrium classification and checkpointing. Effect sizes ($δ=0.37$--$0.78$) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_20633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | rd-spiral: An open-source Python library for learning 2D reaction-diffusion dynamics through pseudo-spectral method Herho, Sandy H. S. Anwar, Iwan P. Suwarman, Rusmawan Pattern Formation and Solitons Computational Physics We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis $>96$) in stable states. Information-theoretic metrics show $10.7\%$ reduction in activator-inhibitor coupling during turbulence versus $6.5\%$ in stable regimes. The solver handles stiffness ratios $>6:1$ with features including automated equilibrium classification and checkpointing. Effect sizes ($δ=0.37$--$0.78$) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics. |
| title | rd-spiral: An open-source Python library for learning 2D reaction-diffusion dynamics through pseudo-spectral method |
| topic | Pattern Formation and Solitons Computational Physics |
| url | https://arxiv.org/abs/2506.20633 |