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When environmental feedback operates more slowly than population growth, the system can undergo boom\u2013bust dynamics, where the population overshoots its carrying capacity and subsequently collapses. In extreme cases, this collapse leads to total extinction. While deterministic models typically fail to capture these finite-time extinction events, we propose a stochastic framework, derived from an individual-based model, to describe boom\u2013bust\u2013extirpation dynamics. We identify a noise-driven, threshold-like behavior where, depending on initial conditions, the population either undergoes a \u201cboom\u201d or is extirpated before the expansion occurs. Furthermore, we characterize a transition between an excitable regime, where most trajectories are captured by the absorbing state immediately after the first bust, and a persistent regime, where most populations reach a metastable state. We show that this transition is governed by the noise strength and the ratio of environmental-to-population timescales. This framework provides a theoretical basis for understanding irreversible transitions in invasive species, plant succession, microbial dynamics, and the elimination of cancerous tumors.<\/jats:p>","DOI":"10.1063\/5.0330931","type":"journal-article","created":{"date-parts":[[2026,9,4]],"date-time":"2026-09-04T13:20:59Z","timestamp":1788528059000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Noise-induced excitability: Bloom, bust, and extirpation in autotoxic population dynamics"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7264-257X","authenticated-orcid":false,"given":"P.","family":"Moreno-Spiegelberg","sequence":"first","affiliation":[{"name":"Department of Agricultural Sciences, University of Naples Federico II 1 , 80055 Portici, Naples,","place":["Italy"]},{"name":"IFISC (CSIC-UIB), Instituto de F\u00edsica Interdisciplinar y Sistemas Complejos 2 , E-07122 Palma de Mallorca,","place":["Spain"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7842-6261","authenticated-orcid":false,"given":"J.","family":"Aguilar","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Astronomia Galileo Galilei, Universit\u00e0 Degli Studi di Padova 3 , via Marzolo 8, 35131 Padova,","place":["Italy"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,4]]},"reference":[{"key":"2026090409203790400_c1","doi-asserted-by":"publisher","first-page":"1337","DOI":"10.1111\/ele.12822","volume":"20","year":"2017","journal-title":"Ecol. 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