Abstract
We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity–mismatch in the intrinsic firing rate of the neurons–can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.
Highlights
We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips
For two coupled neuronal oscillators, described by Eq (1) we study the distribution of the phase differences in the regime of weak coupling and weak noise
As an example of the order induced by inhomogeneity, in this study we have shown that in a minimum system of two synaptically connected neuronal oscillators, more precise relative spike timing can be achieved when the neurons receive different levels of inputs and have different intrinsic firing rates
Summary
We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Synchronous firing of the neurons in one region serves to reliably transmit signals to upstream regions[21,22,23] and synchrony between different regions can prepare dynamic channels for communication[24,25,26] Beyond their functional role, it is important to understand how correlation and synchrony depend on the biophysical parameters of the neurons and the network. Increasing inhomogeneity the effective basin of attraction of the locked state increases and the systems shows more robust locking This results in a sharper probability distribution function (PDF) for the time difference between spiking of two neurons in the presence of weak noise. Biologically realistic phase response curve (PRC), the time difference between the spikes of two neurons in the stable state increases with inhomogeneity, in the case of the leaky integrate-fire (LIF) neurons, they lock in almost zero phase lag for sufficiently small values of inhomogeneity. The synchrony in the general can be assigned both to the inphase firing and to the firing of the neurons with a non-zero phase lag, in the following we call the latter case by “phase-locked” state and use the term “synchronized” for inphase firing of the neurons
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