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

Author(s)

Mirasso, Claudio R. ^[1] ; Carelli, Pedro V. ^[2] ; Pereira, Tiago ^[3] ; Matias, Fernanda S. ^[4] ; Copelli, Mauro ^[2]

Affiliation

^[1] Univ Illes Baleares, CSIC, IFISC, Campus UIB, E-07122 Palma de Mallorca - Spain

^[2] Univ Fed Pernambuco, Dept Fis, Recife, PE - Brazil

^[3] Univ Sao Paulo, Inst Ciencias Matemat & Computacao, Sao Carlos, SP - Brazil

^[4] Univ Fed Alagoas, Dept Fis, Maceio, Alagoas - Brazil

• Document type: Journal article
• Source: Chaos; v. 27, n. 11 NOV 2017.
• Web of Science Citations: 5

Abstract

Anticipated 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. Published by AIP Publishing. (AU)

• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: José Alberto Cuminato
• Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Jefferson Antonio Galves
• Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC