Stochastic difference equations with the Allee effect

Elena Braverman; Alexandra Rodkina

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arXiv · 1606.01928

Stochastic difference equations with the Allee effect

Elena Braverman·Alexandra Rodkina

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Abstract

For a truncated stochastically perturbed equation $x_{n+1}=\max\{ f(x_n)+l\chi_{n+1}, 0 \}$ with $f(x) f(H)>m$. 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 possibly eventually gets into the interval $(0,m-\varepsilon)$, 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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BibTeX RIS

Elena Braverman, Alexandra Rodkina. 2016-06-06. Stochastic difference equations with the Allee effect. https://arxiv.org/abs/1606.01928

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