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Research Article | Open Access

Exploring fractional dynamics in the fractional-in-time Gierer-Meinhardt reaction-diffusion model with periodic boundary condition

Xinzhi Wang1, Wei Zhang2( )
School of Physics and Electronic Information Engineering, Jining Normal University, Ulanqab, Inner Mongolia 012000, China
Institute of Economics and Management, Jining Normal University, Ulanqab, Inner Mongolia 012000, China
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Abstract

This paper presents a new numerical method for simulating the dynamic behavior of the fractional-in-time Gierer-Meinhardt reaction-diffusion model with periodic boundary conditions. A recursive algorithm for binomial coefficients is introduced, avoiding numerical instabilities associated with Gamma functions. High-precision polynomial expansions and the short-memory principle are employed to enhance efficiency and accuracy. Numerical simulations reveal diverse pattern formation.

Keywords

fractional-in-time Gierer-Meinhardt modelpattern formationnumerical methodshort-memory principle

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Networks and Heterogeneous Media
Volume 21 Issue 1,
March 2026
Pages 55-69
DOI: 10.3934/nhm.2026003

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Wang X, Zhang W. Exploring fractional dynamics in the fractional-in-time Gierer-Meinhardt reaction-diffusion model with periodic boundary condition. Networks and Heterogeneous Media, 2026, 21(1): 55-69. https://doi.org/10.3934/nhm.2026003

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Received: 19 August 2025
Revised: 19 December 2025
Accepted: 30 December 2025
Published: 15 March 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)