Du, Zengji; Zhang, Xiaoni; Zhu, Huaiping Dynamics of nonconstant steady states of the Sel’kov model with saturation effect. (English) Zbl 1443.35076 J. Nonlinear Sci. 30, No. 4, 1553-1577 (2020). Summary: 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. Cited in 3 Documents MSC: 35K57 Reaction-diffusion equations 92C15 Developmental biology, pattern formation 92D25 Population dynamics (general) 35Q92 PDEs in connection with biology, chemistry and other natural sciences Keywords:Sel’kov model; saturation law; stability; Turing pattern; nonconstant positive solution PDFBibTeX XMLCite \textit{Z. Du} et al., J. Nonlinear Sci. 30, No. 4, 1553--1577 (2020; Zbl 1443.35076) Full Text: DOI References: [1] Cameron, JB, Spectral collocation and path-following methods for reaction-diffusion equations in one and two space dimensions. Ph.D. thesis, J. Mater. Chem., 3, 975-978 (1994) [2] Davidson, FA; Rynne, BP, A priori bounds and global existence of solutions of the steady-state Sel’kov model, Proc. R. Soc. Edinb. Sect. A, 130, 507-516 (2000) · Zbl 0960.35026 [3] Dutt, AK, Turing pattern amplitude equation for a model glycolytic reaction-diffusion system, J. Math. 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