Abstract
In this paper, we deal with Sel’kov model with saturation law which has been applied to numerous problems in chemistry and biology. We will study the stability of the unique constant steady state, existence and nonexistence of nonconstant steady states of such models. In particular, we prove that Turing pattern may occur when the saturation coefficient is small but will not occur when the coefficient becomes large. Therefore for a Sel’kov model with saturation law, it is the saturation law that determines the formation of spatial patterns.
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Acknowledgements
We express our sincere thanks to the editor and the anonymous reviewers for their valuable comments and suggestions which led to an improvement of our original manuscript and Dr. Shuling Yan for her help in revising the manuscript. This work is partially supported by the Nature Science Foundation of China (Grant Nos. 11871251, 11771185 and 11801231) and NSERC of Canada.
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Du, Z., Zhang, X. & Zhu, H. Dynamics of Nonconstant Steady States of the Sel’kov Model with Saturation Effect. J Nonlinear Sci 30, 1553–1577 (2020). https://doi.org/10.1007/s00332-020-09617-w
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DOI: https://doi.org/10.1007/s00332-020-09617-w