PPubMed8 Dec 2014Cited 23×

Zero-Lag Synchronization Despite Inhomogeneities in a Relay System Study of Synchrony in an Inhomogeneous Relay System

Zahra Ghasemi Esfahani, Alireza Valizadeh, Matjaz Perc

Abstract

A novel proposal for the zero-lag synchronization of the delayed coupled neurons, is to connect them indirectly via a third relay neuron. In this study, we develop a Poincaré map to investigate the robustness of the synchrony in such a relay system against inhomogeneity in the neurons and synaptic parameters. We show that when the inhomogeneity does not violate the symmetry of the system, synchrony is maintained and in some cases inhomogeneity enhances synchrony. On the other hand if the inhomogeneity breaks the symmetry of the system, zero lag synchrony can not be preserved. In this case we give analytical results for the phase lag of the spiking of the neurons in the stable state.

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Zero‑lag synchrony can persist in delayed coupled neurons via a relay neuron if inhomogeneities preserve system symmetry, but breaks when symmetry is violated.

What’s new

i.Developed a Poincaré map to analyze synchrony in a three‑neuron relay system.
ii.Showed that symmetry‑preserving inhomogeneity can maintain or even enhance zero‑lag synchrony.
iii.Provided analytical expressions for phase lag when symmetry is broken.
iv.Compared analytical results with numerical simulations of both phase‑oscillator and Hodgkin‑Huxley neuron models.
v.Identified parameter regimes (frequency mismatch, synaptic strength, delay asymmetry) that affect synchrony.

How they did it

The authors approximated spiking neurons as phase oscillators and modeled synaptic currents as pulsatile stimuli, deriving a Poincaré map for the relay system. They performed numerical simulations, discarding the first 50 periods to avoid transients, and validated the analytical predictions with conductance‑based Hodgkin‑Huxley neuron simulations.

What they found

Synchrony is preserved when inhomogeneity does not break system symmetry, sometimes even improving synchrony.
Zero‑lag synchrony fails when symmetry is broken, leading to predictable phase lags.
Symmetric frequency mismatch allows stable zero‑lag synchrony over a delay‑dependent region.
Asymmetric frequency mismatch eliminates zero‑lag synchrony, yielding only phase‑locked states with non‑zero lag.
Symmetric variations in synaptic strengths can extend stable synchrony to all delay values.

Caveats

✕Analysis relies on phase‑oscillator approximation, which may not capture all dynamics of real neurons.
✕Results depend on the choice of neuronal model; Hodgkin‑Huxley simulations show smaller instability domains.
✕Only a subset of parameter space (delays, mismatches, synaptic strengths) was explored.
✕The study does not address the impact of noise or plasticity on synchrony.

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