In this paper, we are concerned with the Turing instability of the spatially homogeneous Hopf bifurcating periodic solutions for the diffusive Sel’kov model with saturation effect. By using the center manifold theorem, normal form theory and the regularly perturbed theory, we derive a formula in terms of the diffusion rates to determine the Turing instability of the spatially homogeneous Hopf bifurcating periodic solutions in the reaction–diffusion system. Moreover, we compare our results with those of equilibrium solutions to demonstrate the differences between Turing instability of the equilibrium solutions and the periodic solutions.

中文翻译：

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具有饱和效应的扩散 Sel'kov 模型周期解的图灵不稳定性

在本文中，我们关注具有饱和效应的扩散 Sel'kov 模型的空间齐次 Hopf 分叉周期解的图灵不稳定性。通过使用中心流形定理、范式理论和规则扰动理论，我们推导出了一个关于扩散速率的公式，以确定反应扩散系统中空间齐次 Hopf 分叉周期解的图灵不稳定性。此外，我们将我们的结果与平衡解的结果进行比较，以证明平衡解与周期解的图灵不稳定性之间的差异。