Analysis of a non-autonomous mutualism model driven by Levy jumps (Q316866)

A stochastic model for mutualistic biological species population growth devised by the third author et al. [Int. J. Biomath. 8, No. 6, Article ID 1550072, 18 p. (2015; Zbl 1332.34087)] is extended to include abrupt environmental perturbation that is modeled by Lévy noise. For the resulting \(2\times 2\) system of stochastic differential equations, almost sure existence and uniqueness of a positive global solution is proved.NEWLINENEWLINE Theorems are proved that provide conditions under which the solution is stochastically ultimately bounded and conditions under which the solution is stochastically permanent. This paper concludes by proving theorems establishing when the model yields persistence in mean or extinction of one or both of the species.