Iterated function systems of logistic maps: synchronization and intermittency

Neda Abbasi; Masoumeh Gharaei; Ale Jan Homburg

doi:10.1088/1361-6544/aac637

Iterated function systems of logistic maps: synchronization and intermittency

Neda Abbasi, Masoumeh Gharaei, Ale Jan Homburg

Mathematics

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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 language	English
Pages (from-to)	3880-3913
Number of pages	34
Journal	Nonlinearity
Volume	31
Issue number	8
Early online date	9 Jul 2018
DOIs	https://doi.org/10.1088/1361-6544/aac637
Publication status	Published - 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.

Funders	Funder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Keywords

intermittency
iterated function system
logistic family
synchronization

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1088/1361-6544/aac637

Iterated function systems of logistic mapsFinal published version, 860 KBLicence: Article 25fa Dutch Copyright Act

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AU - Abbasi, Neda

AU - Gharaei, Masoumeh

AU - Homburg, Ale Jan

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N2 - 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.

AB - 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.

KW - intermittency

KW - iterated function system

KW - logistic family

KW - synchronization

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Iterated function systems of logistic maps: synchronization and intermittency

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Keywords

UN SDGs

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