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Anticipated and zero-lag synchronization in motifs of delay-coupled systems

AuthorsMirasso, Claudio R. ; Carelli, Pedro V.; Pereira, Tiago; Matias, Fernanda S.
Issue Date11-Oct-2017
PublisherAmerican Institute of Physics
CitationChaos 27(11): 114305 (2017)
AbstractAnticipated and zero-lag synchronization have been observed in different scientific fields. In the brain, they might play a fundamental role in information processing, temporal coding and spatial attention. Recent numerical work on anticipated and zero-lag synchronization studied the role of delays. However, an analytical understanding of the conditions for these phenomena remains elusive. In this paper, we study both phenomena in systems with small delays. By performing a phase reduction and studying phase locked solutions, we uncover the functional relation between the delay, excitation and inhibition for the onset of anticipated synchronization in a sender-receiver-interneuron motif. In the case of zero-lag synchronization in a chain motif, we determine the stability conditions. These analytical solutions provide an excellent prediction of the phase-locked regimes of Hodgkin-Huxley models and Roessler oscillators. Anticipated and zero-lag synchronization are phenomena that are believed to play important roles in the brain, with evidence suggesting that they occur despite the conductance delay between cortical areas. Both synchronization regimes were reported in numerical simulations of motifs of three-node neuronal systems coupled with delay. Here, we present an analytical approach to these problems by performing a phase reduction leading to a phase oscillator model. Since neurons have firing rates of the order of tens of Hertz and conduction delays are in the range of tens of milliseconds, the regime of small delays (less than the period of free-running units) is justified and simplifies the calculations. In this framework, three regimes are predicted to occur as inhibition is increased in a sender-receiver-interneuron (SRI) motif: delayed synchronization (DS), anticipated synchronization (AS), and finally phase drift. Varying the delay in a chain motif of three mutually connected units, on the other hand, the locking between the central and the outer nodes is shown to be close to either in-phase or anti-phase, with instability (phase drift) gaps in-between. The analytical results show very good agreement with numerical simulations of motifs of Hodgkin-Huxley neurons and Roessler oscillators.
Publisher version (URL)https://doi.org/10.1063/1.5006932
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