We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic bursting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance or effectively control the features of the stochastic bursting. The setup can be considered a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noise-induced fluctuations by a corresponding stationary Fokker–Planck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noise-induced switching between a stationary and an oscillatory regime gives rise to stochastic bursting.
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August 2020
Research Article|
August 03 2020
Dynamics of a stochastic excitable system with slowly adapting feedback
Igor Franović
;
Igor Franović
a)
1
Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade
, Pregrevica 118, 11080 Belgrade, Serbia
a)Author to whom correspondence should be addressed: franovic@ipb.ac.rs
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Serhiy Yanchuk
;
Serhiy Yanchuk
b)
2
Institut für Mathematik, Technische Universität Berlin
, Straße des 17. Juni 136, 10623 Berlin, Germany
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Sebastian Eydam
;
Sebastian Eydam
c)
3
Weierstrass Institute
, Mohrenstrasse 39, 10117 Berlin, Germany
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Iva Bačić;
Iva Bačić
d)
1
Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade
, Pregrevica 118, 11080 Belgrade, Serbia
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Matthias Wolfrum
Matthias Wolfrum
e)
3
Weierstrass Institute
, Mohrenstrasse 39, 10117 Berlin, Germany
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a)Author to whom correspondence should be addressed: franovic@ipb.ac.rs
b)
Electronic mail: yanchuk@math.tu-berlin.de
c)
Electronic mail: sebastian.eydam@gmail.com
d)
Electronic mail: iva@scl.rs
e)
Electronic mail: wolfrum@wias-berlin.de
Chaos 30, 083109 (2020)
Article history
Received:
January 15 2020
Accepted:
July 15 2020
Citation
Igor Franović, Serhiy Yanchuk, Sebastian Eydam, Iva Bačić, Matthias Wolfrum; Dynamics of a stochastic excitable system with slowly adapting feedback. Chaos 1 August 2020; 30 (8): 083109. https://doi.org/10.1063/1.5145176
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