A Rulkov neuronal model with Caputo fractional variable-order differences of convolution type

Oana Brandibur , Eva Kaslik , Dorota Mozyrska , Małgorzata Wyrwas


In this paper, a theoretical and numerical investigation is undertaken for a fractional-order version of the Rulkov neuronal model, involving Caputo fractional variable-order differences of convolution type. As a first step, using liniarization techniques and the Z-transform method, sufficient conditions are explored which guarantee the stability or instability of the unique equilibrium point of the system. Numerical simulations are further carried out to illustrate the theoretical findings, emphasizing the differences between the current model and simpler versions involving fractional-order difference with constant fractional orders, as well as the classical integer-order Rulkov model.
Publication typeOriginal work published as abstract
Author Oana Brandibur
Oana Brandibur,,
, Eva Kaslik
Eva Kaslik,,
, Dorota Mozyrska (FCS / DM)
Dorota Mozyrska,,
- Department of Mathematics
, Małgorzata Wyrwas (FCS / DM)
Małgorzata Wyrwas,,
- Department of Mathematics
Publication size in sheets0.3
Book Awrejcewicz Jan, Kaźmierczak M., Mrozowski Jerzy, Olejnik Paweł (eds.): 15th Conference on Dynamical Systems Theory and Applications : DSTA 2019 : abstracts, 2019, Wydawnictwo Politechniki Łódzkiej, ISBN 978-83-66287-28-0, 419 p.
Internal identifierROC 19-20
Languageen angielski
Score (nominal)0
Score sourceconferenceList
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