Exploring fractional dynamics in the fractional-in-time Gierer-Meinhardt reaction-diffusion model with periodic boundary condition
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.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Nonlinear Dynamics and Pattern Formation
Mathematical and Theoretical Epidemiology and Ecology Models
Publication details
- Journal / source
- Networks and Heterogeneous Media
- Volume
- 21
- Issue
- 1
- Pages
- 55–69
- Publication date
- 1 January 2026