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Turing instability-induced oscillations in coupled reaction-diffusion systems |
| Nan Wang(王楠)1, Yuan Tong(仝源)1, Fucheng Liu(刘富成)1,†, Xiaoxuan Li(李晓璇)1, Yafeng He(贺亚峰)1, and Weili Fan(范伟丽)1,2,‡ |
1 College of Physics Science and Technology, Hebei University, Baoding 071002, China;
2 Hebei Province Research Center for Basic Disciplines of Computational Physics, Baoding 071002, China |
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Abstract A new type of localized oscillatory pattern is presented in a two-layer coupled reaction-diffusion system under conditions in which no Hopf instability can be discerned in either layer. The transitions from stationary patterns to asynchronous and synchronous oscillatory patterns are obtained. A novel method based on decomposing coupled systems into two associated subsystems has been proposed to elucidate the mechanism of formation of oscillating patterns. Linear stability analysis of the associated subsystems reveals that the Turing pattern in one layer induces the other layer locally, undergoes a supercritical Hopf bifurcation and gives rise to localized oscillations. It is found that the sizes and positions of oscillations are determined by the spatial distribution of the Turing patterns. When the size is large, localized traveling waves such as spirals and targets emerge. These results may be useful for deeper understanding of pattern formation in complex systems, particularly multilayered systems.
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Received: 21 July 2024
Revised: 22 December 2024
Accepted manuscript online:
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PACS:
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82.40.Ck
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(Pattern formation in reactions with diffusion, flow and heat transfer)
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47.54.-r
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(Pattern selection; pattern formation)
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82.40.Bj
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(Oscillations, chaos, and bifurcations)
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05.65.+b
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(Self-organized systems)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12275065, 12275064, and 12475203), the Natural Science Foundation of Hebei Province (Grant Nos. A2021201010 and A2024201020), Interdisciplinary Research Program of Natural Science of Hebei University (Grant No. DXK202108), Hebei Provincial Central Government Guiding Local Science and Technology Development Funds (Grant No. 236Z1501G), Scientific Research and Innovation Team Foundation of Hebei University (Grant No. IT2023B03), and the Excellent Youth Research Innovation Team of Hebei University (Grant No. QNTD202402). |
Corresponding Authors:
Fucheng Liu, Weili Fan
E-mail: hdlfc@hbu.edu.cn;fanweili@hbu.edu.cn
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Cite this article:
Nan Wang(王楠), Yuan Tong(仝源), Fucheng Liu(刘富成), Xiaoxuan Li(李晓璇), Yafeng He(贺亚峰), and Weili Fan(范伟丽) Turing instability-induced oscillations in coupled reaction-diffusion systems 2025 Chin. Phys. B 34 038201
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