Anticipated Synchronization and Zero-Lag Phases in Population Neural Models

Abstract

Anticipated synchronization is a counterintuitive synchronization regime between a master and a slave dynamical system in which there is a negative phase difference between the driver and the driven system. By studying a set of simple neural oscillators, we unveil the dynamical mechanisms required to generate this phenomenon. We study master–slave configurations where the slave system is, when uncoupled, in a quiescent excitable state. We exemplify our results by describing the dynamics of a dynamical system proposed to model the part of a songbird’s brain involved in song production.

Exploring the Phase-Locking Mechanisms Yielding Delayed and Anticipated Synchronization in Neuronal Circuits

“…This was observed at the three scales that we examined. This result is in agreement with previous studies of AS in a theoretical framework with the explicit time-delay in Equation (1) (Hayashi et al, 2016) and in simplified neural models without the explicit time-delay (Pyragienè and Pyragas, 2013, 2015; Dima et al, 2018).…”

“…Based on previous work on anticipated synchronization in the framework of Equation (1) (Pyragienè and Pyragas, 2013; Hayashi et al, 2016; Dima et al, 2018), we studied the effect that an inhibitory connection and the external current plays in determining the frequency of the receiver system when the sender and the receiver are uncoupled (the receiver free-running frequency ω R ). In fact, we find that both the inhibitory conductance and the external stimuli modify the receiver internal dynamics.…”

“…AS has also been reported in a chain consisting of a sender and two receivers with switching parameters (Pyragienè and Pyragas, 2015), between two Hodgkin-Huxley neurons with different depolarization parameters (Simonov et al, 2014) and in the presence of an inhibitory loop mediated by an interneuron with a free-running frequency greater than the others (Matias et al, 2017). It has also been shown that AS may appear between two neuron models directly coupled provided that the mean frequency of the free receiver is greater than the mean frequency of the sender with (Hayashi et al, 2016) and without the explicit time-delay (Pyragienè and Pyragas, 2013; Dima et al, 2018). AS has been verified in a system in which the delayed feedback has been replaced by a simple, low-order all-pass filter (Pyragiene and Pyragas, 2017).…”

Inhibitory autapse mediates anticipated synchronization between coupled neurons

“…Here we show that AS can occur for firing rates around 20 Hz which means that AS is a robust phenomenon at different time scales. The DS-AS transition could possibly explain commonly reported short latency in visual systems [44][45][46][47][48][49], olfactory circuits [50], songbirds brain [34] and human perception [51,52]. Differently from the first papers about AS [13,23], here the anticipation time is not hardwired in the dynamical equations, but rather emerges from the autapse dynamics.…”

Significant Instances in Motor Gestures of Different Songbird Species

“…Yet, in the mentioned study of juvenile songs [9], neurons in HVC were found bursting simultaneously with the beginning of syllables. In recent work [24], a model with continuous and sparse HVC coding describes the way in which causally connected regions of the song system can display activity simultaneous with the output of the nervous system, after a brief introductory transient. This makes it possible to predict, for example, an important increase of neural activity in the population of projection neurons at the beginning of the whistle syllables in canary song [23,25].…”