Abstract This paper comprehensively considers the two-dimensional spatiotemporal dynamics of the Gierer-Meinhardt model, with the cross-diffusion coefficients as bifurcation parameters. Through multiscale analysis, the amplitude equation at the Turing threshold is derived. The paper sequentially analyzes the effects of cross-diffusion coefficients, Proportional-Derivative controller, fractional diffusion orders, and anisotropy on the system’s stability, pattern formations, and evolution speed. Numerical simulations are provided to validate the conclusions.
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Li et al. (2024) studied this question.
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