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.

中文翻译：

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具有饱和效应的Sel'kov模型的非恒定稳态动力学

在本文中，我们用饱和定律处理Sel'kov模型，该模型已应用于化学和生物学中的许多问题。我们将研究这种模型的唯一恒定稳态的稳定性，非恒定稳态的存在和不存在。特别是，我们证明了当饱和系数较小时可能会出现图灵模式，而在饱和系数较大时不会出现图灵模式。因此，对于具有饱和度定律的Sel'kov模型，正是饱和度定律决定了空间模式的形成。