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Dynamics of stochastic single‐species models
Author(s) -
Zhang Yan,
Lv Jingliang,
Zou Xiaoling
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6540
Subject(s) - mathematics , extinction (optical mineralogy) , stationary distribution , persistence (discontinuity) , stochastic modelling , type (biology) , dynamics (music) , statistical physics , continuous time stochastic process , distribution (mathematics) , stochastic process , mathematical analysis , stochastic differential equation , statistics , ecology , markov chain , paleontology , physics , geotechnical engineering , acoustics , engineering , biology
A type of stochastic single‐species model is proposed and studied. The sufficient conditions of the existence of a unique solution, the existence of its stationary distribution, and stochastic permanence are obtained. Besides, the threshold conditions for its strong stochastic persistence and extinction are found. Finally, some examples and numerical simulations are introduced to support our main results.