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Existence and asymptotic behaviour of positive solutions to a stochastic multispecies Holling type II model
Author(s) -
Xu Ximing,
Xu Libai
Publication year - 2020
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.266
Subject(s) - uniqueness , mathematics , brownian motion , type (biology) , extinction (optical mineralogy) , persistence (discontinuity) , perturbation (astronomy) , statistical physics , mathematical economics , mathematical analysis , ecology , physics , statistics , geology , biology , geotechnical engineering , quantum mechanics , optics
In this paper, we develop a stochastic Holling type II model from the commonly used deterministic Holling type II model by introducing Brownian motion as a stochastic perturbation, which can naturally account for the external environmental effects on a multispecies community. We study the existence and uniqueness of positive solutions to the stochastic model, and we establish sufficient conditions for strong persistence and extinction.