Coexisting Attractors and Multistate Noise-Induced Intermittency in a Cycle Ring of Rulkov Neurons

We study dynamics of a unidirectional ring of three Rulkov neurons coupled by chemical synapses. We consider both deterministic and stochastic models. In the deterministic case, the neural dynamics transforms from a stable equilibrium into complex oscillatory regimes (periodic or chaotic) when the c...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics (Basel) 2023-01, Vol.11 (3), p.597
Main Authors: Bashkirtseva, Irina A., Pisarchik, Alexander N., Ryashko, Lev B.
Format: Article
Language:English
Subjects:
chaos
coupled oscillators
discrete system
Dynamical systems
Equilibrium
Intermittency
Learning models (Stochastic processes)
Mathematics
multistability
Neurons
nonlinear dynamics
Stochastic models
Synapses
Synchronism
Time series
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study dynamics of a unidirectional ring of three Rulkov neurons coupled by chemical synapses. We consider both deterministic and stochastic models. In the deterministic case, the neural dynamics transforms from a stable equilibrium into complex oscillatory regimes (periodic or chaotic) when the coupling strength is increased. The coexistence of complete synchronization, phase synchronization, and partial synchronization is observed. In the partial synchronization state either two neurons are synchronized and the third is in antiphase, or more complex combinations of synchronous and asynchronous interaction occur. In the stochastic model, we observe noise-induced destruction of complete synchronization leading to multistate intermittency between synchronous and asynchronous modes. We show that even small noise can transform the system from the regime of regular complete synchronization into the regime of asynchronous chaotic oscillations.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11030597