Asllani Malbor, Busiello Daniel M, Carletti Timoteo, Fanelli Duccio, Planchon Gwendoline
Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 11, 22100 Como, Italy and Dipartimento di Fisica e Astronomia, University of Florence, INFN and CSDC, Via Sansone 1, 50019 Sesto Fiorentino, Florence, Italy.
Dipartimento di Fisica e Astronomia, University of Florence, INFN and CSDC, Via Sansone 1, 50019 Sesto Fiorentino, Florence, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042814. doi: 10.1103/PhysRevE.90.042814. Epub 2014 Oct 27.
The theory of patterns formation for a reaction-diffusion system defined on a multiplex is developed by means of a perturbative approach. The interlayer diffusion constants act as a small parameter in the expansion and the unperturbed state coincides with the limiting setting where the multiplex layers are decoupled. The interaction between adjacent layers can seed the instability of a homogeneous fixed point, yielding self-organized patterns which are instead impeded in the limit of decoupled layers. Patterns on individual layers can also fade away due to cross-talking between layers. Analytical results are compared to direct simulations.
通过微扰方法建立了在多重结构上定义的反应扩散系统的模式形成理论。层间扩散常数在展开式中作为小参数，未受扰动的状态与多重层解耦的极限情况一致。相邻层之间的相互作用会引发均匀不动点的不稳定性，产生自组织模式，而在层解耦的极限情况下这些模式会受到阻碍。由于层间的串扰，各层上的模式也可能消失。将解析结果与直接模拟结果进行了比较。
