Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure
Abstract
Traveling waves of activity in neural tissue can be halted by spatial inhomogeneity in synaptic coupling. We study an integrate-and-fire network in which each neuron fires once and the coupling decays exponentially. For this model the leading-edge firing map reduces exactly to a scalar equation for the wave speed in space, with a slow unstable and a fast stable homogeneous speed, c1 and c2, and a periodic modulation of the coupling enters this equation pointwise. Positive periodic waves terminate in folds. For slowly varying modulation the fold amplitude approaches a plateau set by the trough of the modulation, where the local bottleneck speed is √(c1 c2); the approach to the plateau is set by the local geometry of the trough. For rapidly varying modulation the fold amplitude grows linearly with frequency, with a slope given by a full-amplitude average over the integrated modulation profile; a weak-ripple truncation of that average overestimates the slope about 2.5-fold at the default coupling. A perturbative recursion in the amplitude gives the speed profile explicitly. We distinguish loss of the periodic wave from failure of a particular launch, and the excitatory regime ε≤ 1 from its sign-changing extension. The results are checked against direct integration of the reduced equation and first-spike firing-map simulations of the network.
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BibTeX
@misc{nissel2026periodically,
title = {{Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure}},
author = {Jie Nissel and Ricardo Erazo-Toscano and Rosahn Bhattarai and Marius Osan and Mandeep Chauhan and Remus Osan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33006},
eprint = {2609.33006},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33006},
}
RIS
TY - UNPB
TI - Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure
AU - Jie Nissel
AU - Ricardo Erazo-Toscano
AU - Rosahn Bhattarai
AU - Marius Osan
AU - Mandeep Chauhan
AU - Remus Osan
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.33006
UR - https://arxiv.org/abs/2609.33006
AB - Traveling waves of activity in neural tissue can be halted by spatial inhomogeneity in synaptic coupling. We study an integrate-and-fire network in which each neuron fires once and the coupling decays exponentially. For this model the leading-edge firing map reduces exactly to a scalar equation for the wave speed in space, with a slow unstable and a fast stable homogeneous speed, c_1 and c_2, and a periodic modulation of the coupling enters this equation pointwise. Positive periodic waves terminate in folds. For slowly varying modulation the fold amplitude approaches a plateau set by the trough of the modulation, where the local bottleneck speed is √(c_1 c_2); the approach to the plateau is set by the local geometry of the trough. For rapidly varying modulation the fold amplitude grows linearly with frequency, with a slope given by a full-amplitude average over the integrated modulation profile; a weak-ripple truncation of that average overestimates the slope about 2.5-fold at the default coupling. A perturbative recursion in the amplitude gives the speed profile explicitly. We distinguish loss of the periodic wave from failure of a particular launch, and the excitatory regime ε≤ 1 from its sign-changing extension. The results are checked against direct integration of the reduced equation and first-spike firing-map simulations of the network.
ER -