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January  2008, 9(1): 145-162. doi: 10.3934/dcdsb.2008.9.145

Phase-locking and Arnold coding in prototypical network topologies

Stefan Martignoli 1, and  Ruedi Stoop 2,

1. 

Institute for Neuroinformatics UZH/ETHZ, Winterthurerstrasse 190, 8057 Zürich, Switzerland
2. 

Institute of Neuroinformatics UZH/ETHZ, Winterthurerstrasse 190, 8057 Zürich, Switzerland

Received  August 2006 Revised  July 2007 Published  October 2007

Phase-and-frequency-locking phenomena among coupled biological oscillators are a topic of current interest, in particular to neuroscience. In the case of mono-directionally pulse-coupled oscillators, phase-locking is well understood, where the phenomenon is globally described by Arnold tongues. Here, we develop the tools that allow corresponding investigations to be made for more general pulse-coupled networks. For two bi-directionally coupled oscillators, we prove the existence of three-dimensional Arnold tongues that mediate from the mono- to the bi-directional coupling topology. Under this transformation, the coupling strength at which the onset of chaos is observed is invariant. The developed framework also allows us to compare information transfer in feedforward versus recurrent networks. We find that distinct laws govern the propagation of phase-locked spike-time information, indicating a qualitative difference between classical artificial vs. biological computation.
Keywords: Arnold tongues, recurrent topology., phase-locked oscillators.
Mathematics Subject Classification: Primary: 37E10; Secondary: 37E4.
Citation: Stefan Martignoli, Ruedi Stoop. Phase-locking and Arnold coding in prototypical network topologies. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 145-162. doi: 10.3934/dcdsb.2008.9.145
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