Dependence of initial value and adaptive adjustment on pattern formation for the coupled discrete diffusion system

Li Xu^{a,b,/sup>, Jing Du^c,*}

ABSTRACT: Turing patterns formation may depend on variation of the initial conditions. In this work, the dependent mechanism of initial distributions on pattern formation for the coupled discrete diffusion system is discussed, some asymptotic behavior between pattern formation and initial value determined by the corresponding eigenvectors of the eigenvalue for discrete Laplace operator can be given. To control the coupled discrete diffusion system for pattern selection, an adaptive adjustment mechanism is applied, and some theoretical generalizations are obtained. Then, the effectiveness of the theory analysis is validated though simulation results.

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^a	School of Technology, Lishui University, Lishui 323000 China
^b	School of Science, Tianjin University of Commerce, Tianjin 300130 China
^c	School of Medicine, Lishui University, Lishui 323000 China

* Corresponding author, E-mail: bettyhappy409@163.com

Received 4 Aug 2022, Accepted 2 Sep 2023

Dependence of initial value and adaptive adjustment on pattern formation for the coupled discrete diffusion system

Li Xua,b,/sup>, Jing Duc,*

Li Xu^{a,b,/sup>, Jing Du^c,*}