Ring of map-based neural oscillators: From order to chaos and back

•A ring of map-based Rulkov neural models is considered.•Corporate effects “chaos-order” are demonstrated.•A synchronization of chaotic oscillators is studied. We study transitions from regular to chaotic dynamics and back of a ring of three map-based neurons with parameter mismatch. First, we consi...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2020-07, Vol.136, p.109830, Article 109830
Main Authors: Bashkirtseva, Irina A., Ryashko, Lev B., Pisarchik, Alexander N.
Format: Article
Language:English
Subjects:
Chaos
Coupling
Lyapunov exponent
Neuron-like oscillator
Rulkov map
Spiking
Synchronization
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Summary:•A ring of map-based Rulkov neural models is considered.•Corporate effects “chaos-order” are demonstrated.•A synchronization of chaotic oscillators is studied. We study transitions from regular to chaotic dynamics and back of a ring of three map-based neurons with parameter mismatch. First, we consider the case when each neuron being isolated is in a stable equilibrium and show that an increase in the coupling strength can lead to chaotic dynamics following a quasiperiodic behavior. Then, we consider the case when the uncoupled neurons are in a chaotic state and demonstrate the route from chaos to periodicity as the coupling strength is increased. We show that this interesting effect results from lag synchronization of the coupled neural oscillators. The system stability is characterized by the largest Lyapunov exponents in the space of the coupling strength and parameter mismatch, while lag synchronization is measured using the similarity function.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2020.109830