Extreme value theory for synchronization of coupled map lattices

D. Faranda (1, 2) , H. Ghoudi (3, 4, 5) , P. Guiraud (6, 7) , Sandro Vaienti (4, 5)

1 LSCE - Laboratoire des Sciences du Climat et de l'Environnement [Gif-sur-Yvette]
2 ESTIMR - Extrèmes : Statistiques, Impacts et Régionalisation
3 LDSC - Laboratory of Dynamical Systems and Combinatorics
4 CPT - Centre de Physique Théorique - UMR 7332
5 CPT - E7 Systèmes dynamiques : théories et applications
6 CIMFAV - Centro de Investigación y Modelamiento de Fenómenos Aleatorios – Valparaíso
7 Laboratoire ORSOX

We show that the probability of appearance of synchronisation in chaotic coupled map lattices is related to the distribution of the maximum of a certain observable evaluated along almost all orbit. We show that such distribution belongs to the family of extreme value laws, whose parameters, namely the extremal index, allow us to get a detailed description of the probability of synchronisation. Theoretical results are supported by robust numerical computations that allow to go beyond the theoretical framework provided and are potentially applicable to physically relevant systems.

Domaines: Systèmes dynamiques [math.DS]; Dynamique Chaotique [nlin.CD]

D. Faranda, H. Ghoudi, P. Guiraud, Sandro Vaienti. Extreme value theory for synchronization of coupled map lattices. Nonlinearity, 2018, 31 (7), pp.3326-3358. ⟨10.1088/1361-6544/aabc8e⟩. ⟨hal-01768182⟩