Details
 Project's acronym:
 SpaceTop
 Financial Program Name:
 SHENG
 Organization:
 Narodowe Centrum Nauki (NCN) (National Science Centre)
 Agreement:
 UMO2018/30/Q/ST1/00228 z dnia 20190726
 Realisation period:
 20190726  20240725
 Research team leader:
 prof. dr hab. Grzegorz Graff
 Realised in:
 Department of Differential Equations and Mathematical Applications
 External institutions
participating in project: 
 Academy of Mathematics and Systems Science, Chinese Academy of Sciences. (China)
 Project's value:
 1 215 893.06 PLN
 Request type:
 International Research Programmes
 Domestic:
 International project
 Verified by:
 Gdańsk University of Technology
Papers associated with that project
Filters
total: 7
Catalog Projects
Year 2024

Algebraic periods and minimal number of periodic points for smooth selfmaps of 1connected 4manifolds with definite intersection forms
PublicationLet M be a closed 1connected smooth 4manifolds, and let r be a nonnegative integer. We study the problem of finding minimal number of rperiodic points in the smooth homotopy class of a given map f: M>M. This task is related to determining a topological invariant D^4_r[f], defined in Graff and Jezierski (Forum Math 21(3):491–509, 2009), expressed in terms of Lefschetz numbers of iterations and local fixed point indices of...

An absorbing set for the Chialvo map
PublicationThe 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...
Year 2023

Attractors of dissipative homeomorphisms of the infinite surface homeomorphic to a punctured sphere
PublicationA 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 homeomorphisms at a fixed point, namely the existence of socalled inverse saddle, impacts thetopology of the attractor — it cannot be arcwise connected

Topologicalnumerical analysis of a twodimensional discrete neuron model
PublicationWe conduct computerassisted analysis of a twodimensional 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 setoriented 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...
Year 2021

Dold sequences, periodic points, and dynamics
PublicationIn this survey we describe how the socalled Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.

Persistent homology as a new method of the assessment of heart rate variability
PublicationHeart 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...
Year 2020

Computations of the least number of periodic points of smooth boundarypreserving selfmaps of simplyconnected manifolds
PublicationLet $r$ be an odd natural number, $M$ a compact simplyconnected smooth manifold, $\dim M\geq 4$, such that its boundary $\partial M$ is also simplyconnected. We consider $f$, a $C^1$ selfmaps of $M$, preserving $\partial M$. In [G. Graff and J. Jezierski, Geom. Dedicata 187 (2017), 241258] 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...
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