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We investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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 adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
In some applications not only the knowledge of the behaviour of trajectories of a map is important, but also their displacements. We describe in detail the distribution of elements of the displacement sequence along a trajectory of an orientation preserving circle homeomorphism ϕ with irrational rotation number ϱ(ϕ). The values of displacement are dense in a set which depends on the map γ (semi-)conjugating ϕ with the rotation...
My research interests include:
· dynamical systems, chaos theory, topological methods in dynamical systems
· application of dynamical systems theory to modelling of biological phenomena, especially applications
I am currently an assistant professor (adjunct) at Gdansk University of Technology (Department of Differential Equations and Mathematics Applications). My scientific interests include dynamical systems theory, chaos theory and their applications to modeling of biological phenomena, especially to neurosciences.
In June 2013 I completed PhD in Mathematics at the Institute of Mathematics of Polish Academy of Sciences (IMPAN) (thesis title: “Dynamical properties of maps arising in some models of neuron activity and electrical circuits”; advisors: W. Marzantowicz (Adam Mickiewicz University in Poznań) and F. Przytycki (IMPAN, Warsaw)). After that I spent another year at IMPAN in Warsaw at the position of Assistant Professor in the Dynamical Systems Group.
Next I worked as a post-doctoral researcher at INRIA - Paris Centre and the Mathematical Neuroscience Team at CIRB – Collège de France, in the project “Complex oscillations in neuronal systems”.
Uzyskane stopnie/tytuły naukowe
Nadanie stopnia naukowegodr Matematyka (Dziedzina nauk matematycznych)Instytut Matematyczny PAN
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