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Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure — arXiv:2609.33006

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.33006
License (as archived): CC0-1.0
Archived: 2026-10-08T01:04:04.485Z
SHA-256 of the archived text: 21062471a7895d39ad7837463e8da12904f5d9533d724dd54e9ea1f73df85e19
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How to cite

Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure — arXiv:2609.33006 — arXiv (en), https://arxiv.org/abs/2609.33006 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eebb14ddb866 (Metraipolis archive dc_eebb14ddb866, sha256 21062471a7895d39ad7837463e8da12904f5d9533d724dd54e9ea1f73df85e19)

BibTeX

@misc{dceebb14ddb866,
  title = {Periodically modulated traveling waves in integrate-and-fire networks: recursive speed law and propagation failure — arXiv:2609.33006},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.33006},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eebb14ddb866; sha256 21062471a7895d39ad7837463e8da12904f5d9533d724dd54e9ea1f73df85e19},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.33006. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $\sqrt{c_1 c_2}$; 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 $\epsilon\le 1$ 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.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-29 in cond-mat.stat-mech).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Disordered Systems and Neural Networks (cond-mat.dis-nn); Pattern Formation and Solitons (nlin.PS); Neurons and Cognition (q-bio.NC).
Pagina del lavoro: https://arxiv.org/abs/2609.33006 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-08T00:43:12.908Z dalla pagina https://arxiv.org/catchup/cond-mat.stat-mech/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).