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

Author

Listed:
  • Famei Zheng

    (Huaiyin Normal University)

  • Guixin Hu

    (Henan Polytechnic University)

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.

Suggested Citation

  • Famei Zheng & Guixin Hu, 2022. "Dynamical Behaviors of a Stochastic Single-Species Model with Allee Effects," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1553-1563, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09874-6
    DOI: 10.1007/s11009-021-09874-6
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    References listed on IDEAS

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    1. Li, Dagen & Liu, Meng, 2020. "Invariant measure of a stochastic food-limited population model with regime switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 16-26.
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