During the past decades, pattern formulation with reaction–diffusion systems has attracted great research interest. Complex networks, from single-layer networks to more complicated multiplex networks, have made great contribution to the development of this area, especially with emergence of Turing patterns. While among vast majority of existing works on multiplex networks, they only take into account the simple case with ordinary diffusion, which is termed as self-diffusion. However, cross-diffusion, as a significant phenomenon, reveals the direction of species’ movement, and is widely found in chemical, biological and physical systems. Therefore, we study the pattern formulation on multiplex networks with the presence of both self-diffusion and cross-diffusion. Of particular interest, heterogeneous patterns with abundant characteristics are generated, which cannot arise in other systems. Through linear analysis, we theoretically derive the Turing instabilities region. Besides, ...

中文翻译：

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复用网络上的交叉扩散

在过去的几十年中，具有反应扩散系统的模式制定引起了极大的研究兴趣。从单层网络到更复杂的多路复用网络的复杂网络为该领域的发展做出了巨大贡献，特别是随着图灵模式的出现。尽管在现有的大多数复用网络作品中，它们仅考虑了具有普通扩散的简单情况，这被称为自扩散。但是，交叉扩散是一种重要现象，它揭示了物种运动的方向，并广泛存在于化学，生物和物理系统中。因此，我们研究存在自扩散和交叉扩散的多重网络上的模式制定。特别感兴趣的是 生成具有丰富特征的异构模式，这在其他系统中不会出现。通过线性分析，我们从理论上推导了图灵不稳定性区域。再说...