4 papers
Linear relations modulo meager sets
Marek Balcerzak, Paolo Leonetti
We prove several topological zero-one laws. First, we show that, if a subset of a Banach space has the Baire property, then admits a somewhere dense set of vectors $x \…
Astrocytes: Arnol'd Tongues Generalization in Dynamical Systems' Parameter Plane
Gonzalo Marcelo RamÃrez-Ãvila, S. Leo Kingston, Marek Balcerzak +3
We discovered generalized structures, named astrocytes due to their shape, that constitute a defined region characterizing regular behavior within the parameter plane (PP) of dynam…
Electronic Equivalent of a Mechanical Impact Oscillator
Volodymyr Denysenko, Marek Balcerzak, Artur Dabrowski
This paper presents a novel design of an electronic circuit that is equivalent to a mechanical discontinuous impact oscillator exhibiting hard impacts. The governing equations of t…
Master Stability Function for networks of coupled non-smooth oscillators
Volodymyr Denysenko, Marek Balcerzak, Artur Dabrowski
This paper describes extension of the Master Stability Function for arrays of non-smooth oscillators. This extension is based on the previously introduced Jacobi matrix estimation…