Turing pattern of the Oregonator model |
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Authors: | Rui Peng Fuqin Sun |
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Institution: | a Institute of Nonlinear Complex Systems, College of Science, China Three Gorges University, Yichang 443002, Hubei, PR China b School of Science and Technology, University of New England, Armidale, NSW, 2351, Australia c Department of Mathematics and Physics, Tianjin University of Technology and Education, Tianjin 300222, PR China |
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Abstract: | The Oregonator model is the mathematical dynamics which describes the Field-Körös-Noyes mechanics of the famous Belousov-Zhabotinskii? reaction. In this work, we establish some fundamental analytic properties of this dynamics and its corresponding steady state. Under various conditions on the parameters and the size of the reactor, we examine the existence and non-existence of non-constant steady states. In particular, for some properly chosen parameter ranges, we prove the occurrence of the Turing pattern generated by this Oregonator model. Our results exhibit interesting and very different roles of the diffusion rates and the reactor in the formation of the Turing pattern. Our mathematical analysis mainly relies on a priori estimates and the topological degree argument. |
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Keywords: | 35J55 35K57 92C15 92C40 |
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