Synchronization versus stability of the invariant distribution for a class of globally coupled maps

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Bálint P, Keller G, Mincsovicsne Selley F, Tóth IP
Zeitschrift: Nonlinearity
Jahr der Veröffentlichung: 2018
Band: 31
Heftnummer: 8
ISSN: 0951-7715
Sprache: Englisch


Abstract

We study a class of globally coupled maps in the continuum limit,
where the individual maps are expanding maps of the circle. The circle
maps in question are such that the uncoupled system admits a unique
absolutely continuous invariant measure, which is furthermore mixing.
Interaction arises in the form of diffusive coupling, which involves a
function that is discontinuous on the circle. We show that for
sufficiently small coupling strength the coupled map system admits a
unique absolutely continuous invariant distribution, which depends on
the coupling strength ε. Furthermore, the invariant density
exponentially attracts all initial distributions considered in our
framework. We also show that the dependence of the invariant density on
the coupling strength ε is Lipschitz continuous in the BV norm.

When
the coupling is sufficiently strong, the limit behavior of the system
is more complex. We prove that a wide class of initial measures approach
a point mass with support moving chaotically on the circle. This can be
interpreted as synchronization in a chaotic stat


FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Keller, Gerhard Prof. Dr.
Professur für Mathematik (Ergodentheorie)
Mincsovicsne Selley, Fanni
Professur für Mathematik (Ergodentheorie)


Einrichtungen weiterer Autorinnen und Autoren

Budapest University of Technology and Economics (BME) / Budapesti Műszaki és Gazdaságtudományi Egyetem


Zitierweisen

APA:
Bálint, P., Keller, G., Mincsovicsne Selley, F., & Tóth, I.P. (2018). Synchronization versus stability of the invariant distribution for a class of globally coupled maps. Nonlinearity, 31(8). https://dx.doi.org/10.1088/1361-6544/aac5b0

MLA:
Bálint, Péter, et al. "Synchronization versus stability of the invariant distribution for a class of globally coupled maps." Nonlinearity 31.8 (2018).

BibTeX: 

Zuletzt aktualisiert 2019-05-01 um 01:10