19 citations · 67 across the 9 of their papers we have counts for
9 papers
Analysis of the Chaotic Itinerancy Phenomenon using Entropy and Clustering
Nikodem Mierski, Paweł Pilarczyk
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine s…
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…
Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate - blood pressure coupling quantified by entropy-based indices
Paweł Pilarczyk, Grzegorz Graff, José M. Amigó +3
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…
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…
Rigorous computation of escape times for parameter intervals in the quadratic map
Paweł Pilarczyk, Stefano Luzzatto
We study the quadratic family of one-dimensional maps . We conduct comprehensive numerical analysis of collections of finite orbits of the critical point, comput…
Rigorous numerics for critical orbits in the quadratic family
Ali Golmakani, Comlan Edmond Koudjinan, Stefano Luzzatto +1
We develop algorithms and techniques to compute rigorous bounds for finite pieces of orbits of the critical points, for intervals of parameter values, in the quadratic family of on…
Uniform expansivity outside the critical neighborhood in the quadratic family
Ali Golmakani, Stefano Luzzatto, Paweł Pilarczyk
We use rigorous numerical techniques to compute a lower bound for the exponent of expansivity outside a neighborhood of the critical point for thousands of intervals of parameter v…
Inducing a map on homology from a correspondence
Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow +1
We study the homomorphism induced in homology by a closed correspondence between topological spaces, using projections from the graph of the correspondence to its domain and codoma…
Finite Resolution Dynamics
Stefano Luzzatto, Pawel Pilarczyk
We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system havin…