Abstract
A stochastic single-species model with Allee effects under regime switching is developed and detected in the present study. First, extinction and persistence of the model are dissected. Subsequently, sufficient criteria are offered to ensure that the model possesses a unique ergodic stationary distribution. Finally, the theoretical outcomes are employed to evaluate the evolution of the African wild dog (Lycaon pictus) in Africa, and some significant functions of stochastic perturbations are exposed.
Highlights
The Allee effect, which is depicted by a relationship between the per capita growth rate and the population size, is a universal biological phenomenon [2, 11, 14]
The significance of Allee effects has been admitted in a lot of biological subjects, and numerous mathematical frameworks have been put forward to dissect the role of Allee effects
The present study detects these behaviors of (2): we first dissect the extinction and persistence of model (2) in Sect. 2, and offer sufficient criteria to ensure that model (3) possesses a unique ergodic stationary distribution (UESD) in Sect. 3; in Sect. 4, we make use of the theoretical outcomes to evaluate the evolution of the African wild dog (Lycaon pictus) in Africa and expose some significant functions of puny undulations and medium undulations
Summary
The Allee effect, which is depicted by a relationship between the per capita growth rate and the population size, is a universal biological phenomenon [2, 11, 14]. Several authors (see, e.g., [1, 9, 10, 15,16,17]) have proffered that the puny undulations often act on the parameters in a system, and one could take advantage of the white noise to approximately depict the puny undulations. Choristoneura fumiferana (Clemens) reproduces 50% more eggs at 25◦C than at 15◦C [3] These medium undulations cannot be portrayed by (2) [12, 15,16,17]. The present study detects these behaviors of (2): we first dissect the extinction and persistence of model (2) in Sect. 2, and offer sufficient criteria to ensure that model (3) possesses a unique ergodic stationary distribution (UESD) in Sect. 3; in Sect. 4, we make use of the theoretical outcomes to evaluate the evolution of the African wild dog (Lycaon pictus) in Africa and expose some significant functions of puny undulations and medium undulations
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