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.

Turing patterns in multiplex networks / Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - STAMPA. - 90:(2014), pp. 042814-042814. [10.1103/PhysRevE.90.042814]

Turing patterns in multiplex networks

ASLLANI, MALBOR;FANELLI, DUCCIO;
2014

Abstract

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.
2014
90
042814
042814
Asllani, Malbor; Busiello, Daniel M.; Carletti, Timoteo; Fanelli, Duccio; Planchon, Gwendoline
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1011221
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