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

Bálint P, Keller G, Mincsovicsne Selley F, Tóth IP (2018)

Publication Language: English

Publication Type: Journal article

Publication year: 2018

Journal

Nonlinearity Institute of Physics: Hybrid Open Access

Book Volume: 31

Journal Issue: 8

DOI: 10.1088/1361-6544/aac5b0

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

Authors with CRIS profile

Gerhard Keller Professur für Angewandte Mathematik (Angewandte Analysis) Fanni Mincsovicsne Selley Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

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

How to cite

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).

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