Analysis of a stochastic autonomous mutualism model

作者：Liu Meng^*; Wang Ke

来源：Journal of Mathematical Analysis and Applications, 2013, 402(1): 392-403.

DOI：10.1016/j.jmaa.2012.11.043

• Lotka-Volterra mutualism model
• Random perturbation
• Permanence
• Extinction
• Global asymptotic stability

An autonomous Lotka-Volterra mutualism system with random perturbations is investigated. Under some simple conditions, it is shown that there is a decreasing sequence {Delta(k)} which has the property that if Delta(1) < 1, then all the populations go to extinction (i.e. lim(t ->infinity) x(i)(t)(_)= 0, 1 < i <= n); if Delta(k) > 1 > Delta(k+1), then lim(t ->infinity) x(j)(t) = 0, j = k + 1, ..., n, whilst the remaining k populations are stable in the mean (i.e., lim(t ->infinity) t(-1) integral(t)(0) x(i)(s) ds = a positive constant, i = 1, ..., k); if Delta(n) > 1, then all the species are stable in the mean. Sufficient conditions for stochastic permanence and global asymptotic stability are also established.

• 出版日期2013-6-1
• 单位淮阴师范学院; 哈尔滨工业大学