Iterated function systems of logistic maps: synchronization and intermittency

Neda Abbasi, Masoumeh Gharaei, Ale Jan Homburg

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Abstract

We discuss iterated function systems generated by finitely many logistic maps, with a focus on synchronization and intermittency. We provide sufficient conditions for synchronization, involving negative Lyapunov exponents and minimal dynamics. A number of results that clarify the scope of these conditions are included. We analyze a mechanism for intermittency that involves the full map x → 4x(1 - x) as one of the generators of the iterated function system. For iterated function systems generated by x → 2x(1 - x) and x → 4x(1 - x) we prove the existence of a σ-finite stationary measure.

Original languageEnglish
Pages (from-to)3880-3913
Number of pages34
JournalNonlinearity
Volume31
Issue number8
Early online date9 Jul 2018
DOIs
Publication statusPublished - Aug 2018

Funding

This work is partly financed by the Netherlands Organisation for Scientific Research (NWO). NA is also grateful for the hospitality of the Korteweg-de Vries Institute for Mathematics.

FundersFunder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek

    Keywords

    • intermittency
    • iterated function system
    • logistic family
    • synchronization

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