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17 papers · 1 filter
Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model
Dorian Falęcki, Mikołaj Rosman, Michał Palczewski +2
We conduct a topological--numerical analysis of global dynamics in a discrete-time two-gene Andrecut--Kauffman model. This model describes gene expression regulation through nonlin…
Rigorous computation of expansion in one-dimensional dynamics
Paweł Pilarczyk, Michał Palczewski, Stefano Luzzatto
We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and th…
Dold coefficients of quasi-unipotent homeomorphisms of orientable surfaces
Grzegorz Graff, Wacław Marzantowicz, Łukasz Patryk Michalak
The sequence of Dold coefficients of a self-map forms a dual sequence to the sequence of Lefschetz numbers of iterations of under the Mö…
Every finite set of natural numbers is realizable as algebraic periods of a Morse$\unicode{x2013}$Smale diffeomorphism
Grzegorz Graff, Wacław Marzantowicz, Łukasz Patryk Michalak +1
A given self-map of a compact manifold determines the sequence of the Lefschetz numbers of its iterations. We consider its dual sequence give…
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…
Testing topological conjugacy of time series
Paweł Dłotko, Michał Lipiński, Justyna Signerska-Rynkowska
This paper considers a problem of testing, from a finite sample, a topological conjugacy of two dynamical systems and . More precisely, given $x_1,\ldots, x_n \subse…