Math. Model. Nat. Phenom.
Volume 12, Number 4, 2017Complex Dynamics, Synchronization, and Emergent Behaviour in Neural Systems and Networks
|Page(s)||74 - 90|
|Published online||03 July 2017|
Stochastic Sensitivity Analysis of Noise-Induced Mixed-Mode Oscillations in Morris--Lecar Neuron Model
Institute of Mathematics and Computer Sciences, Ural Federal University Lenina, 51, 620000, Ekaterinburg, Russia
* Corresponding author. E-mail: Evdokia.Slepukhina@urfu.ru
The effect of noise on the two-dimensional Morris--Lecar neuron model is studied. In the deterministic case, this system exhibits mono- and bistable dynamic regimes. In the parametric zone, where the stable equilibrium and the stable limit cycle coexist, the phenomenon of noise-induced transitions between the attractors is investigated. In the parametric zone of monostability, when the single attractor of the deterministic system is the stable equilibrium, the stochastic generation of large amplitude oscillations is also observed. We show that under the stochastic disturbances, in both cases the system demonstrates noise-induced mixed-mode oscillations, i.e., the alternation of small and large amplitude oscillations. For the parametric analysis of this phenomenon, an approach combining stochastic sensitivity function technique, confidence domains and Mahalanobis distance methods is suggested.
Mathematics Subject Classification: 37H20 / 60H10
Key words: Morris–Lecar model / excitability / stochastic sensitivity / noise-induced mixed-mode oscillations
© EDP Sciences, 2017
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