Informacje szczegółowe
- Akronim projektu:
- SpaceTop
- Program finansujący:
- SHENG konkurs na polsko-chińskie projekty badawcze
- Instytucja:
- Narodowe Centrum Nauki (NCN) (National Science Centre)
- Porozumienie:
- UMO-2018/30/Q/ST1/00228 z dnia 2019-07-26
- Okres realizacji:
- 2019-07-26 - 2024-07-25
- Kierownik zespołu badawczego:
- prof. dr hab. Grzegorz Graff
- Realizowany w:
- Katedra Równań Różniczkowych i Zastosowań Matematyki
- Instytucje zewnętrzne
biorące udział w projekcie: -
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences. (Chiny)
- Wartość projektu:
- 1 215 893.06 PLN
- Typ zgłoszenia:
- Międzynarodowy Program Badawczy
- Pochodzenie:
- Projekt zagraniczny/międzynarodowy
- Weryfikacja:
- Politechnika Gdańska
Publikacje powiązane z tym projektem
Filtry
wszystkich: 6
Katalog Projektów
Rok 2020
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Computations of the least number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublikacjaLet $r$ be an odd natural number, $M$ a compact simply-connected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simply-connected. We consider $f$, a $C^1$ self-maps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241-258] the smooth Nielsen type periodic number $D_r(f;M,\partial M)$ was defined and proved to be equal to the minimal number of $r$-periodic points...
Rok 2021
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Persistent homology as a new method of the assessment of heart rate variability
PublikacjaHeart rate variability (hrv) is a physiological phenomenon of the variation in the length of the time interval between consecutive heartbeats. In many cases it could be an indicator of the development of pathological states. The classical approach to the analysis of hrv includes time domain methods and frequency domain methods. However, attempts are still being made to define new and more effective hrv assessment tools. Persistent...
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Dold sequences, periodic points, and dynamics
PublikacjaIn this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.
Rok 2023
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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...
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Attractors of dissipative homeomorphisms of the infinite surface homeomorphic to a punctured sphere
PublikacjaA class of dissipative orientation preserving homeomorphisms of the infinite annulus,pairs of pants, or generally any infinite surface homeomorphic to a punctured sphere isconsidered. We prove that in some isotopy classes the local behavior of such homeomor-phisms at a fixed point, namely the existence of so-called inverse saddle, impacts thetopology of the attractor — it cannot be arcwise connected
Rok 2024
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An absorbing set for the Chialvo map
PublikacjaThe classical Chialvo model, introduced in 1995, is one of the most important models that describe single neuron dynamics. In order to conduct effective numerical analysis of this model, it is necessary to obtain a rigorous estimate for the maximal bounded invariant set. We discuss this problem, and we correct and improve the results obtained by Courbage and Nekorkin (2010). In particular, we provide an explicit formula for an...
wyświetlono 593 razy