A class of hyperbolic reaction–diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics.

Linear stability analysis on the uniform steady states is performed to derive the conditions for the occurrence of Hopf, Turing and wave instabilities. The weakly nonlinear analysis is then employed to describe the time evolution of the pattern amplitude close to the stability threshold. The effects of the inertial times on the pattern formation as well as on the transient regimes are highlighted. As an illustrative example, our analysis is applied to the prototype Schnakenberg model and the theoretical results are illustrated both analytically and numerically.

一类具有交叉扩散的双曲反应扩散模型是在扩展热力学的背景下得出的。

对均匀稳态进行线性稳定性分析，以得出发生霍普夫，图灵和波不稳定性的条件。然后采用弱非线性分析来描述接近稳定阈值的模式幅度的时间演化。突出了惯性时间对图形形成以及瞬态状态的影响。举一个说明性的例子，我们的分析被应用于原型Schnakenberg模型，并且理论上的分析和数值都得到了说明。