17 citations · 40 across the 5 of their papers we have counts for
4 papers · 1 filter
Fixed point indices of iterates of orientation-reversing homeomorphisms
Grzegorz Graff, Patryk Topór
We show that any sequence of integers satisfying necessary Dold's congruences is realized as the sequence of fixed point indices of the iterates of an orientation-reversing homeomo…
An absorbing set for the Chialvo map
Paweł Pilarczyk, Grzegorz Graff
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…
Topological-numerical analysis of a two-dimensional discrete neuron model
Paweł Pilarczyk, Justyna Signerska-Rynkowska, Grzegorz Graff
We conduct computer-assisted analysis of the two-dimensional model of a neuron introduced by Chialvo in 1995 (Chaos, Solitons & Fractals 5, 461-479). We apply the method for rigoro…
Dold sequences, periodic points, and dynamics
Jakub Byszewski, Grzegorz Graff, Thomas Ward
In this survey we describe how the so-called Dold congruence arises in topology, and how it relates to periodic point counting in dynamical systems.