{"paper":{"title":"Stochastic difference equations with the Allee effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandra Rodkina, Elena Braverman","submitted_at":"2016-06-06T20:19:16Z","abstract_excerpt":"For a truncated stochastically perturbed equation $x_{n+1}=\\max\\{ f(x_n)+l\\chi_{n+1}, 0 \\}$ with $f(x)<x$ on $(0,m)$, which corresponds to the Allee effect, we observe that for very small perturbation amplitude $l$, the eventual behavior is similar to a non-perturbed case: there is extinction for small initial values in $(0,m-\\varepsilon)$ and persistence for $x_0 \\in (m+\\delta, H]$ for some $H$ satisfying $H>f(H)>m$. As the amplitude grows, an interval $(m-\\varepsilon, m+\\delta)$ of initial values arises and expands, such that with a certain probability, $x_n$ sustains in $[m, H]$, and possib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01928","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"}