On a population model with Allee effects and environmental perturbations

The present study takes advantage of the white noise and the Lévy noise to portray the small and sudden environmental perturbations respectively, and puts forward a stochastic population model with Allee effects and Lévy jumps. First, it is confirmed that the model possesses a unique, global and pos...

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Bibliographic Details
Published inJournal of applied mathematics & computing Vol. 64; no. 1-2; pp. 749 - 764
Main Author Ji, Weiming
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2020
Springer Nature B.V
Subjects
Applied mathematics
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Noise
Original Research
Population
Stochastic models
Theory of Computation
White noise
Allee effects
60H10
60H30
92D25
Extinction
Permanence
Environmental perturbations
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Summary:The present study takes advantage of the white noise and the Lévy noise to portray the small and sudden environmental perturbations respectively, and puts forward a stochastic population model with Allee effects and Lévy 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 Lévy 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 .
ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-020-01377-w