Dynamical Behaviors of a Stochastic Single-Species Model with Allee Effects

Famei Zheng and Guixin Hu ()
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Famei Zheng: Huaiyin Normal University
Guixin Hu: Henan Polytechnic University

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1553-1563

Abstract: Abstract In this letter, we test a scalar stochastic nonlinear equation used to portray the growth of a population with Allee effects. We first testify that there is a unique dynamical bifurcation point Λ to the equation, and the sign of Λ determines the dynamical properties of the equation: if Λ is negative, then the equation has a unique invariant measure — the Dirac measure concentrated at zero; if Λ is positive, the equation has a unique invariant measure concentrated on ( 0 , + ∞ ) $(0,+\infty )$ , and the density function of the invariant measure can be expressed explicitly. Then we probe the lower-growth rate and the continuity of the solution. Finally, we apply the theoretical results to research the growth of African hunting dogs.

Keywords: Allee principle; Stochasticity; Dynamical bifurcation; Stability; 60H10; 60H30; 92D25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09874-6

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