• Previous Article
    The patch recovery for finite element approximation of elasticity problems under quadrilateral meshes
  • DCDS-B Home
  • This Issue
  • Next Article
    Noncoercive damping in dynamic hemivariational inequality with application to problem of piezoelectricity
January  2008, 9(1): 145-162. doi: 10.3934/dcdsb.2008.9.145

Phase-locking and Arnold coding in prototypical network topologies

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.
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
[1]

Tian Ma, Shouhong Wang. Topological phase transition III: Solar surface eruptions and sunspots. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020350

[2]

Helmut Abels, Andreas Marquardt. On a linearized Mullins-Sekerka/Stokes system for two-phase flows. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020467

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (67)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]