13 citations · 17 across the 6 of their papers we have counts for
10 papers
Subthreshold oscillations and spiking in hybrid neuron models with a dynamic threshold
Piotr Bartłomiejczyk, Juan Belmonte-Beitia, Justyna Signerska-Rynkowska
We investigate a class of two-dimensional hybrid non-autonomous periodically forced neuron models known as the Meng-Huguet-Rinzel neuron model, with a dynamic threshold and reset m…
Dynamic threshold curves and response precision in forced excitable systems
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan Touboul
We investigate here various properties of the responses of excitable systems subject to periodic forcing and noise. While the properties of intrinsic oscillators, subject to added…
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…
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…
Periodic and chaotic dynamics in a map-based neuron model
Frank Llovera Trujillo, Justyna Signerska-Rynkowska, Piotr Bartłomiejczyk
Map-based neuron models are an important tool in modelling neural dynamics and sometimes can be considered as an alternative to usually computationally costlier models based on con…
Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models
Jonathan Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul
Experimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretic…
Curlicues generated by circle homeomorphisms
Justyna Signerska-Rynkowska
We investigate the curves in the complex plane which are generated by sequences of real numbers being the lifts of the points on the orbit of an orientation preserving circle homeo…
Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike adding and chaos
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan D. Touboul +1
In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and…
Integrate-and-fire models with an almost periodic input function
Piotr Kasprzak, Adam Nawrocki, Justyna Signerska-Rynkowska
We investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and -almost periodic functions. Special attention is paid to the properties of a firing…
Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
Jonathan E. Rubin, Justyna Signerska-Rynkowska, Jonathan Touboul +1
This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation a…