Topological and numerical methods in dynamical systems

In the framework of the project, new mathematical methods for algorithmic analysis of dynamical systems will be developed, based on computational topology and rigorous numerical methods. Publications in high quality academic journals are planned, as well as active participation in national and international conferences, collaboration with domestic and foreign scientists (Spain, Italy, Japan), short-term visits of the participants of the project in other academic centers in Poland and abroad, as well as visits of invited scientists at Gdańsk Tech. A few months long scholarships for students are planned. It is expected that the scope of the undertaken activities will have positive influence on the image of Gdańsk Tech as a Research Institute.

Details

Financial Program Name:: OPUS
Organization:: Narodowe Centrum Nauki (NCN) (National Science Centre)
Agreement:: UMO-2021/41/B/ST1/00405 z dnia 2021-11-26
Realisation period:: 2021-11-26 - 2025-10-12
Project manager:: dr hab. Paweł Pilarczyk
Realised in:: Department Of Differential Equations And Mathematical Applications
Project's value:: 376 370.00 PLN
Request type:: National Research Programmes
Domestic:: Domestic project
Verified by:: Gdańsk University of Technology

Papers associated with that project

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total: 4

Year 2025

Bistability and chaos in the discrete two-gene Andrecut-Kauffman model
Publication
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B - Year 2025
We conduct numerical analysis of the 2-dimensional discrete-time gene expression model originally introduced by Andrecut and Kauffman (Phys. Lett. A 367: 281–287, 2007). In contrast to the previous studies, we analyze the dynamics with different reaction rates α1 and α2 for each of the two genes under consideration. We explore bifurcation diagrams for the model with α1 varying in a wide range and α2 fixed. We detect chaotic dynamics...

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Year 2024

An absorbing set for the Chialvo map
Publication
- P. Pilarczyk
- G. Graff
- Communications in Nonlinear Science and Numerical Simulation - Year 2024
The 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...

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Year 2023

Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy-based indices
Publication
- P. Pilarczyk
- G. Graff
- J. Amigo
- K. Tessmer
- K. Narkiewicz
- K. Narkiewicz
- B. Graff
- CHAOS - Year 2023
We introduce an entropy-based classification method for pairs of sequences (ECPS) for quantifying mutual dependencies in heart rate and beat-to-beat blood pressure recordings. The purpose of the method is to build a classifier for data in which each item consists of two intertwined data series taken for each subject. The method is based on ordinal patterns and uses entropy-like indices. Machine learning is used to select a subset...

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Topological-numerical analysis of a two-dimensional discrete neuron model
Publication
- CHAOS - Year 2023
We 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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