On a population model with Allee effects and environmental perturbations

• DOI: 10.1007/s12190-020-01377-w
• Publication Date: 2020-06-23T02:02:42Z
• Authors: Weiming Ji
• Keywords: 0101 mathematics; 01 natural sciences

The present study takes advantage of the white noise and the Levy noise to portray the small and sudden environmental perturbations respectively, and puts forward a stochastic population model with Allee effects and Levy jumps. First, it is confirmed that the model possesses a unique, global and positive solution. Then, permanence and extinction of the species are examined. Afterwards, the trajectory of population abundance is tested. The findings uncover that both the white noise and the Levy noise have significant functions on the rate of population change. Finally, the theoretical findings are applied to dissect the rate of population change of the African hunting dog Lycaon pictus.