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 | |
| 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 |
|---|
| Nederlandse Organisatie voor Wetenschappelijk Onderzoek |
UN SDGs
This output contributes to the following UN Sustainable Development Goals (SDGs)
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SDG 7 Affordable and Clean Energy
Keywords
- intermittency
- iterated function system
- logistic family
- synchronization
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