Measuring transient chaos in nonlinear one- and two-dimensional maps |
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| Affiliation: | 1. Faculty of Mathematics, Physics and Informatics, University of Gdansk, Gdansk 80-308, Poland;2. Faculty of Electronics, Telecommunications, and Informatics, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland;1. Université de Limoges, LCSN, EA 1069, F-87000 Limoges, France;2. Université de Monastir, Laboratoire de Physico-chimie des Matériaux, Faculté des Sciences de Monastir, Tunisie;3. Molecular Tumorigenesis and Anticancer Pharmacology, EDST, Lebanese University, Hadath, Lebanon;1. School of Pharmacy, Guangdong Medical University, Zhanjiang 524023, China;2. Analysis Centre of Guangdong Medical University, Zhanjiang 524023, China;3. Guangdong Key Laboratory for Research and Development of Nature Drugs, Guangdong Medical University, Zhanjiang 524023, China;4. The First Clinical Medical College, Guangdong Medical University, Zhanjiang 524023, China;1. Instituto Federal de Educação, Ciência e Tecnologia de Mato Grosso do Sul, R. Salime Tanure, s/n, 79400-000 Coxim, MS, Brazil;2. Grupo de Pesquisa em Síntese e Caracterização Molecular, Faculdade de Ciências Exatas e Tecnologia, Universidade Federal da Grande Dourados, R. João Rosa Góes, 1761, 79825-070 Dourados, MS, Brazil;3. Centro de Pesquisa e Tecnologia em Recursos Naturais, Universidade Estadual de Mato Grosso do Sul, R. Emílio Mascoli, 275, 79950-000 Naviraí, MS, Brazil;4. Universidade Tecnológica Federal do Paraná, Av. Monteiro Lobato, 1787, 84016210 Ponta Grossa, PR, Brazil;5. Departamento de Química, Universidade Federal de Santa Maria, Av. Roraima, 1000, 97105-900 Santa Maria, RS, Brazil |
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| Abstract: | In this paper, we present results of numerical experiments on chaotic transients in families of the logistic and Hénon maps. The duration of chaotic transients (the rambling time) for logistic maps estimated according to a rigorous criterion shows monotonic regularities with respect to both the period and the number of periodic window in a series of a given period. Due to inapplicability of this criterion to multidimensional maps, a more universal, though approximate, criterion is systematically studied on the family of logistic maps to optimize a choice of the free parameter value. The same approximate criterion is used to estimate rambling time for a number of periodic windows for the family of Hénon maps. The dependence of the rambling time on the width of periodic windows is tested. |
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