This paper focuses on the role of hyperbolicity on pattern formation in the subcritical regime for a class of hyperbolic models with cross-diffusion. A weakly nonlinear analysis up to the fifth order is employed to describe the time evolution of the pattern amplitude close to the instability threshold. The effects of the inertial times on the pattern formation as well as on the transient subcritical regime are investigated, both analitically and numerically, in the case of the hyperbolic Schnakenberg model.

中文翻译：

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具有双扩散的双曲模型中的亚临界图灵模式

本文着重研究了双曲模型在亚临界状态下对于一类具有交叉扩散的双曲模型的作用。采用微弱的非线性分析，直至五阶，以描述接近不稳定性阈值的图案振幅的时间演化。在双曲线Schnakenberg模型的情况下，无论是从数值上还是从惯性上，都以分析和数值方式研究了惯性时间对图形形成以及瞬态亚临界状态的影响。