Turing pattern dynamics in a fractional-diffusion oregonator model under PD control
In this paper, fractional-order diffusion and proportional-derivative (PD) control are introduced in oregonator model, and the Turing pattern dynamics is investigated for the first time. We take the cross-diffusion coefficient as the bifurcation parameter and give some necessary conditions for Turi...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2025-02-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/38967 |
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| Summary: | In this paper, fractional-order diffusion and proportional-derivative (PD) control are introduced in oregonator model, and the Turing pattern dynamics is investigated for the first time. We take the cross-diffusion coefficient as the bifurcation parameter and give some necessary conditions for Turing instability of the fractional-diffusion oregonator model under PD control. At the same time, we construct the amplitude equations near the bifurcation threshold and determine the pattern formation of the fractional-diffusion oregonator model under PD controller. It is observed by numerical simulations that in the absence of control, the pattern formation changes with the variation of the cross-diffusion coefficient in two-dimensional space. Meanwhile, it is verified that the PD control has a significant impact on Turing instability, and the pattern structure can be changed by manipulating the control gain parameters for the fractional-diffusion oregonator model.
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| ISSN: | 1392-5113 2335-8963 |