A stochastic predator-prey system with stage structure for predator. (English) Zbl 1474.92091

Summary: The authors introduce stochasticity into a predator-prey system with Beddington-DeAngelis functional response and stage structure for predator. We present the global existence and positivity of the solution and give sufficient conditions for the global stability in probability of the system. Numerical simulations are introduced to support the main theoretical results.


92D25 Population dynamics (general)
34F05 Ordinary differential equations and systems with randomness
Full Text: DOI


[1] Beddington, J. R., Mutual interference between parasities and its effect on searching efficiency, Journal of Animal Ecology, 44, 331-341 (1975) · doi:10.2307/3866
[2] DeAngelis, D. L.; Goldsten, R. A.; Neil, R., A model for trophic interaction, Ecology, 56, 88-92 (1975)
[3] Georgescu, P.; Hsieh, Y.-H., Global dynamics of a predator-prey model with stage structure for the predator, SIAM Journal on Applied Mathematics, 67, 5, 1379-1395 (2007) · Zbl 1120.92045 · doi:10.1137/060670377
[4] May, R. M., Stability and Complexity in Model Ecosystems (2001), Princeton, NJ, USA: Princeton University Press, Princeton, NJ, USA · Zbl 1044.92047
[5] Liu, M.; Wang, K., Global stability of stage-structured predator-prey models with Beddington-DeAngelis functional response, Communications in Nonlinear Science and Numerical Simulation, 16, 9, 3792-3797 (2011) · Zbl 1219.92064 · doi:10.1016/j.cnsns.2010.12.026
[6] Liu, M.; Wang, K., Analysis of a stochastic autonomous mutualism model, Journal of Mathematical Analysis and Applications, 402, 392-403 (2013) · Zbl 1417.92141 · doi:10.1016/j.jmaa.2012.11.043
[7] Liu, M.; Wang, K., Stochastic Lotka-Volterra systems with Lévy noise, Journal of Mathematical Analysis and Applications, 410, 2, 750-763 (2014) · Zbl 1327.92046 · doi:10.1016/j.jmaa.2013.07.078
[8] Mao, X., Stochastic Differential Equations and Their Applications (1997), Chichester, UK: Horwood, Chichester, UK · Zbl 0892.60057
[9] Mao, X., Stochastic versions of the LaSalle theorem, Journal of Differential Equations, 153, 1, 175-195 (1999) · Zbl 0921.34057 · doi:10.1006/jdeq.1998.3552
[10] Higham, D. J., An algorithmic introduction to numerical simulation of stochastic differential equations, SIAM Review, 43, 3, 525-546 (2001) · Zbl 0979.65007 · doi:10.1137/S0036144500378302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.