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Published on: September 5, 2019
A time independent least squares algorithm for parameter identification of Turing patterns in reaction-diffusion
Lili Chang1,2, Xinyu Wang3,4, Guiquan Sun5,6
1Complex Systems Research Center, Shanxi University, Taiyuan, 030006, China. changll@amss.ac.cn.
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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