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Multilevel regularity of orbits of expanding Lorenz maps with application to the Courbage-Nekorkin-Vdovin model
Abstract
We discuss the structure and properties of itineraries of periodic orbits for expanding Lorenz maps with nontrivial rotation interval. In particular, it is shown that periodic orbits of such maps are organized in two cascades (called Stern-Brocot and Geller-Misiurewicz cascades), which are closely related to the Farey tree of rational rotation numbers of a given map. The obtained results are illustrated with a reduced Courbage-Nekorkin-Vdovin neuron model, allowing us to characterize regularity of periodic spiking patterns in the model.
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Authors (3)
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Piotr Nowak-Przygodzki
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.3934/dcdsb.2025076
- License
- Copyright (American Institute of Mathematical Sciences)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
no. 30,
pages 4185 - 4205,
ISSN: 1531-3492 - Language:
- English
- Publication year:
- 2025
- Bibliographic description:
- Bartłomiejczyk P., Nowak-Przygodzki P., Signerska-Rynkowska J.: Multilevel regularity of orbits of expanding Lorenz maps with application to the Courbage-Nekorkin-Vdovin model// DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B -Vol. 30,iss. 11 (2025), s.4185-4205
- DOI:
- Digital Object Identifier (open in new tab) 10.3934/dcdsb.2025076
- Sources of funding:
-
- Free publication
- Verified by:
- Gdańsk University of Technology
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