Wyszukiwarka
Informacje szczegółowe
- Program finansujący:
- SONATA
- Instytucja:
- Narodowe Centrum Nauki (NCN) (National Science Centre)
- Porozumienie:
- UMO-2019/35/D/ST1/02253 z dnia 2020-06-25
- Okres realizacji:
- 2020-06-25 - 2025-06-24
- Kierownik projektu:
- dr inż. Justyna Signerska-Rynkowska
- Członkowie zespołu:
-
- stypendysta-doktorant Frank Llovera Trujillo
- Kierownik projektu dr inż. Justyna Signerska-Rynkowska
- Realizowany w:
- Zakład Równań Różniczkowych i Zastosowań Matematyki
- Wartość projektu:
- 258 360.00 PLN
- Typ zgłoszenia:
- Krajowy Program Badawczy
- Pochodzenie:
- Projekt krajowy
- Weryfikacja:
- Politechnika Gdańska
Publikacje powiązane z tym projektem
Filtry
wszystkich: 6
Katalog Projektów
Rok 2024
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Analysis of dynamics of a map-based neuron model via Lorenz maps
PublikacjaModeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large...
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Testing Topological Conjugacy of Time Series
PublikacjaThis paper considers a problem of testing, from a finite sample, a topological conjugacy of two trajectories coming from dynamical systems (X, f ) and (Y, g). More precisely, given x1, . . . , xn \subset X and y1, . . . , yn \subset Y such that xi+1 = f (xi) and yi+1 = g(yi) as well as h : X \rightarrow Y, we deliver a number of tests to check if f and g are topologically conjugated via h. The values of the tests are close to...
Rok 2023
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Periodic and chaotic dynamics in a map‐based neuron model
PublikacjaMap-based neuron models are an important tool in modeling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on continuous or hybrid dynamical systems. However, due to their discrete nature, rigorous mathematical analysis might be challenging. We study a discrete model of neuronal dynamics introduced by Chialvo in 1995. In particular, we show that its reduced one-dimensional...
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Spike patterns and chaos in a map-based neuron model
PublikacjaThe work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour....
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Topological-numerical analysis of a two-dimensional discrete neuron model
PublikacjaWe conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461–479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757–789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times...
Rok 2022
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Curlicues generated by circle homeomorphisms
PublikacjaWe investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeomorphism. Geometrical properties of these curves such as boundedness, superficiality, local discrete radius of curvature are linked with dynamical properties of the circle homeomorphism which generates them: rotation number and its continued fraction...
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