Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity

@article{Heitmann2015SynchronyWA,
  title={Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity},
  author={Stewart Heitmann and Bard Ermentrout},
  journal={Biological Cybernetics},
  year={2015},
  volume={109},
  pages={333-347}
}
Spatiotemporal waves of synchronized activity are known to arise in oscillatory neural networks with lateral inhibitory coupling. How such patterns respond to dynamic changes in coupling strength is largely unexplored. The present study uses analysis and simulation to investigate the evolution of wave patterns when the strength of lateral inhibition is varied dynamically. Neural synchronization was modeled by a spatial ring of Kuramoto oscillators with Mexican hat lateral coupling. Broad bands… Expand
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References

SHOWING 1-10 OF 37 REFERENCES
A computational role for bistability and traveling waves in motor cortex
TLDR
It is surmise that motor cortex may employ state-dependent computation to achieve very rapid changes between bistable motor states when the demand for speed exceeds the demands for accuracy. Expand
Traveling Electrical Waves in Cortex Insights from Phase Dynamics and Speculation on a Computational Role
TLDR
It is suggested that the continuum of phase shifts during epochs with traveling waves provides a means to scan the incoming sensory stream for novel features in order to understand the traveling electrical waves that are observed across olfactory, visual, and visuomotor areas of cortex. Expand
Spiral Waves in Disinhibited Mammalian Neocortex
TLDR
Stable rotating spiral waves are reported in rat neocortical slices visualized by voltage-sensitive dye imaging and it is speculated that rotating spiral Waves may provide a spatial framework to organize cortical oscillations. Expand
Synchrony in Excitatory Neural Networks
TLDR
It is shown that excitation is generally desynchronizing for neurons with a response of type I but can be synchronizing for responses of type II when the synaptic interactions are fast, and even beyond the weak coupling regime. Expand
Dynamics of pattern formation in lateral-inhibition type neural fields
  • S. Amari
  • Mathematics, Medicine
  • Biological Cybernetics
  • 2004
TLDR
The dynamics of pattern formation is studied for lateral-inhibition type homogeneous neural fields with general connections and it is proved that there are five types of pattern dynamics. Expand
Hippocampal theta oscillations are travelling waves
TLDR
The results demonstrate that theta oscillations pattern hippocampal activity not only in time, but also across anatomical space, and the presence of travelling waves indicates that the instantaneous output of the hippocampus is topographically organized and represents a segment of physical space. Expand
Waves and stimulus-modulated dynamics in an oscillating olfactory network.
TLDR
The application of natural odor stimuli causes the electrical activity along the lobe to transiently switch from the state with propagating waves to one with spatially uniform oscillations, and the behavioral and computational relevance of this change in global timing is discussed. Expand
Propagating Waves of Activity in the Neocortex: What They Are, What They Do
TLDR
The development of voltage-sensitive dyes and fast optical imaging techniques have brought a new tool for examining spatiotemporal patterns of population neuronal activity in the neocortex, and wave dynamics as an emergent behavior of the population activity that can, in turn, influence the activity of individual neurons are discussed. Expand
The dynamics of chimera states in heterogeneous Kuramoto networks
Abstract We study a variety of mixed synchronous/incoherent (“chimera”) states in several heterogeneous networks of coupled phase oscillators. For each network, the recently-discovered Ott–AntonsenExpand
Pattern Formation in an Array of Oscillators with Electrical and Chemical Coupling
TLDR
It is shown thathibitory synapses and electrical synapses have different synchronizing properties and can cause a bifurcation to a patterned state from synchrony which ultimately develops into traveling waves. Expand
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