{"paper":{"title":"Firing map of an almost periodic input function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"(2) Institute of Mathematics, Adam Mickiewicz University of Poznan, Computer Sci., J. Signerska (2) ((1) Faculty of Mathematics, Polish Academy of Sciences), W. Marzantowicz (1)","submitted_at":"2011-06-16T19:12:01Z","abstract_excerpt":"In mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system \\dot{x}= f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model \\dot{x}=f(t) still hold if f \\in L_{loc}^1(R) and f is an almost periodic function. Moreover, in this way we prepare a formal framework for next study of a discrete dynamics "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3309","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"}