Persistence and nonpersistence of a nonautonomous stochastic mutualism system
type: Item
instance of: scholarly article
title: Persistence and nonpersistence of a nonautonomous stochastic mutualism system
zbMATH Open document ID: 1402.92375
DOI: 10.1155/2013/256249
author: Peiyan Xia
author: Xiaokun Zheng
author: Daqing Jiang
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: In this paper, a two-species nonautonomous stochastic mutualism system is investigated. The intrinsic growth rates of the two species at time \(t\) are estimated by \(r_i(t) + \sigma_i(t)\dot{B}_i(t), i = 1, 2\) respectively. Viewing the different intensities of the noises \(\sigma_i(t), i = 1, 2\) as two parameters at time \(t\), we conclude that there exists a global positive solution and the \(p\)th moment of the solution is bounded. We also show that the system is permanent, including stochastic permanence, persistence in mean, and asymptotic boundedness in time average. Besides, we show that the large white noise will make the system nonpersistent. Finally, we establish sufficient criteria for the global attractivity of the system.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 6161315
zbMATH Keywords: nonautonomous stochastic mutualism system
Wikidata QID: Q58915693
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/256249
OpenAlex ID: W1973611137
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description: scientific article; zbMATH DE number 6161315