A Rulkov neuronal model with Caputo fractional variable-order differences of convolution type
Oana Brandibur , Eva Kaslik , Dorota Mozyrska , Małgorzata Wyrwas
AbstractIn 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 size in sheets||0.3|
|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 identifier||ROC 19-20|
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