Liu, Qun; Jiang, Daqing; Hayat, Tasawar; Alsaedi, Ahmed Dynamical behavior of stochastic predator-prey models with distributed delay and general functional response. (English) Zbl 1444.92092 Stochastic Anal. Appl. 38, No. 3, 403-426 (2020). Summary: In this article, we study two stochastic predator-prey models with distributed delay and general functional response. For the nonautonomous periodic case of the system, by utilizing Khasminskii’s theory of periodic solution, we prove that the system admits a positive \(T\)-periodic solution. For the system which is perturbed by both white and colored noises, we establish sufficient conditions for the existence of positive recurrence of the solutions to the system. The existence of positive recurrence implies stochastic weak stability. Cited in 5 Documents MSC: 92D25 Population dynamics (general) 34K13 Periodic solutions to functional-differential equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:stochastic predator-prey model; general functional response; distributed delay; periodic solution; positive recurrence PDFBibTeX XMLCite \textit{Q. Liu} et al., Stochastic Anal. Appl. 38, No. 3, 403--426 (2020; Zbl 1444.92092) Full Text: DOI References: [1] May, R. M., Stability and Complexity in Model Ecosystems (1973), New Jersey: Princeton University Press, New Jersey [2] Freedman, H. I., Deterministic mathematical models in population ecology, Biometrics, 22, 219-236 (1980) · Zbl 0448.92023 [3] Liu, W.; Jiang, Y., Bifurcation of a delayed Gause predator-prey model with Michaelis-Menten type harvesting, J. Theor. Biol., 438, 116-132 (2018) · Zbl 1394.92109 [4] Chen, L., Mathematical Models and Methods in Ecology (1988), Beijing: Science Press, Beijing [5] Gause, G. 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