Abstract
Turing patterns arising from reaction–diffusion systems such as epidemic, ecology or chemical reaction models are an important dynamic property. Parameter identification of Turing patterns in spatial continuous and networked reaction–diffusion systems is an interesting and challenging inverse problem. The existing algorithms require huge account operations and resources. These drawbacks are amplified when apply them to reaction–diffusion systems on large-scale complex networks. To overcome these shortcomings, we present a new least squares algorithm which is rooted in the fact that Turing patterns are the stationary solutions of reaction–diffusion systems. The new algorithm is time independent, it translates the parameter identification problem into a low dimensional optimization problem even a low order linear algebra equations. The numerical simulations demonstrate that our algorithm has good effectiveness, robustness as well as performance.
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (Grant Nos. 12022113, 62025602, 12231012), the Basic Applied Study Program of Shanxi Province (Grant No. 20210302123453), the Key Research and Development Preject of Lvliang (Grant No. 2022GXYF18), and the Health Commission of Shanxi Province (Grant No. 2020XM18).
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LC and XW designed the study, performed the numerical simulations, all authors wrote and edited the manuscript.
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Chang, L., Wang, X., Sun, G. et al. A time independent least squares algorithm for parameter identification of Turing patterns in reaction–diffusion systems. J. Math. Biol. 88, 5 (2024). https://doi.org/10.1007/s00285-023-02026-z
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DOI: https://doi.org/10.1007/s00285-023-02026-z