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Publication Type
Journal Article
UWI Author(s)
Author, Analytic
Braverman, E; Rodkina, Alexandra E
Author Affiliation, Ana.
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Article Title
Stochastic difference equations with the Allee effect
Medium Designator
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Connective Phrase
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Journal Title
Discrete and Continuous Dynamical Systems
Translated Title
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Reprint Status
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Date of Publication
2016
Volume ID
36
Issue ID
11
Page(s)
5929-2949
Language
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Connective Phrase
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Location/URL
https:; arxiv.org/pdf/1606.01928.pdf
ISSN
n/a
Notes
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Abstract
For a truncated stochastically perturbed equation xn+1 = max{f(xn)+l?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 - e) and persistence for x0 ? (m + d, H] for some H satisfying H > f(H) > m. As the amplitude grows, an interval (m-e, m+d) of initial values arises and expands, such that with a certain probability, xn sustains in [m, H], and possibly eventually gets into the interval (0, m- e), with a positive probability. Lower estimates for these probabilities are presented. If H is large enough, as the amplitude of perturbations grows, the Allee effect disappears: a solution persists for any positive initial value....
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Keywords