{"paper":{"title":"Population Dynamics of Globally Coupled Degrade-and-Fire Oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"math.CA","authors_text":"Alex Blumenthal, Bastien Fernandez","submitted_at":"2014-11-06T13:07:39Z","abstract_excerpt":"This paper reports the analysis of the dynamics of a model of pulse-coupled oscillators with global inhibitory coupling. The model is inspired by experiments on colonies of bacteria-embedded synthetic genetic circuits. The total population can be either of finite (arbitrary) size or infinite, and is represented by a one-dimensional profile. Profiles can be discontinuous, possibly with infinitely many jumps. Their time evolution is governed by a singular differential equation. We address the corresponding initial value problem and characterize the dynamics' main features. In particular, we prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1595","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}