Asymptotic Properties of a Stochastic Predator-Prey Model with Bedding-DeAngelis Functional Response
In this paper, a stochastic predator-prey system with Bedding-DeAngelis functional response is studied. By constructing a suitable Lyapunov founction, sufficient conditions for species to be stochastically permanent is established. Meanwhile, we show that the species will become extinct with probability one if the noise is sufficiently large.
[1] M. Liu and K. Wang, Global stability of a nonlinear stochastic predatorprey
system with Beddington-DeAngelis functional response, Commun.
Nonlinear Sci. Numer. Simulat, 2011, 16, 1114-1121.
[2] C. Ji, D. Q. Jiang and X. Li, Qualitative analysis of a stochastic ratiodependent
predator-prey system, Journal of Computational and Applied
Mathematics, 2011, 235, 1326-1341.
[3] J. Lv and K. Wang, Asymptotic properties of a stochastic predator-prey
system with Holling II functional response, Commun Nonlinear Sci
Numer Simulat, 2011, 16, 4037-4048.
[4] D. Q. Jiang, N. Shi and X. Li, Global stability and stochastic permanence
of a non-autonomous logistic equation with random perturbation, J.
Math. Anal. Appl, 2008, 340, 588-597.
[5] C. Ji, D. Q. Jiang and N. Jiang, Analysis of a predator-prey model
with modified Leslie-Gower and Holling-type II schemes with stochastic
perturbation, J Math Anal Appl, 2009, 359, 482-498.
[6] Z. Xing, J. Peng, Boundedness, persistence and extinction of a stochastic
non-autonomous logistic system with time delays, Applied Mathematical
Modelling, 2012, 36, 3379C3386.
[7] M. Liu and K. Wang, Extinction and permanence in a stochastic nonautonomous
population system, Applied Mathematics Letters, 2010,
23, 1464C1467.
[8] M. Liu and K. Wang, Global asymptotic stability of a stochastic
LotkaCVolterra model with infinite delays, Commun Nonlinear Sci
Numer Simulat, 2012, 17, 3115C3123.
[9] M. Liu and K. Wang, On a stochastic logistic equation with impulsive
perturbations, Computers and Mathematics with Applications, 2012,
63, 871C886.
[10] C. Zhu and G. Yin, On competitive LotkaCVolterra model in random
environments, J. Math. Anal. Appl., 2009, 357, 154C170.
[11] M. Liu and K. Wang, Persistence and extinction in stochastic nonautonomous
logistic systems, J. Math. Anal. Appl., 2011, 375, 443C457.
[12] X. Liu, S. Zhong, B. Tian, F. Zheng, Asymptotic properties
of a stochastic predator-prey model with Crowley-Martin functional
response, Journal of Applied Mathematics and Computing (2013)
doi:10.1007/s12190-013-0674-0.
[13] X. Liu, S. Zhong, F. Zhong, Z. Liu, Properties of a stochastic predatorprey
system with Holling II functional response, Inter. J. Math. Sci., 2013,
7, 73-79.
[14] X. Li, X Mao. Population dynamical behavior of non-autonomous Lotka-
Volterra competitive system with random perturbation. Discrete Contin
Dyn Syst, 2009;24:523-545.
[1] M. Liu and K. Wang, Global stability of a nonlinear stochastic predatorprey
system with Beddington-DeAngelis functional response, Commun.
Nonlinear Sci. Numer. Simulat, 2011, 16, 1114-1121.
[2] C. Ji, D. Q. Jiang and X. Li, Qualitative analysis of a stochastic ratiodependent
predator-prey system, Journal of Computational and Applied
Mathematics, 2011, 235, 1326-1341.
[3] J. Lv and K. Wang, Asymptotic properties of a stochastic predator-prey
system with Holling II functional response, Commun Nonlinear Sci
Numer Simulat, 2011, 16, 4037-4048.
[4] D. Q. Jiang, N. Shi and X. Li, Global stability and stochastic permanence
of a non-autonomous logistic equation with random perturbation, J.
Math. Anal. Appl, 2008, 340, 588-597.
[5] C. Ji, D. Q. Jiang and N. Jiang, Analysis of a predator-prey model
with modified Leslie-Gower and Holling-type II schemes with stochastic
perturbation, J Math Anal Appl, 2009, 359, 482-498.
[6] Z. Xing, J. Peng, Boundedness, persistence and extinction of a stochastic
non-autonomous logistic system with time delays, Applied Mathematical
Modelling, 2012, 36, 3379C3386.
[7] M. Liu and K. Wang, Extinction and permanence in a stochastic nonautonomous
population system, Applied Mathematics Letters, 2010,
23, 1464C1467.
[8] M. Liu and K. Wang, Global asymptotic stability of a stochastic
LotkaCVolterra model with infinite delays, Commun Nonlinear Sci
Numer Simulat, 2012, 17, 3115C3123.
[9] M. Liu and K. Wang, On a stochastic logistic equation with impulsive
perturbations, Computers and Mathematics with Applications, 2012,
63, 871C886.
[10] C. Zhu and G. Yin, On competitive LotkaCVolterra model in random
environments, J. Math. Anal. Appl., 2009, 357, 154C170.
[11] M. Liu and K. Wang, Persistence and extinction in stochastic nonautonomous
logistic systems, J. Math. Anal. Appl., 2011, 375, 443C457.
[12] X. Liu, S. Zhong, B. Tian, F. Zheng, Asymptotic properties
of a stochastic predator-prey model with Crowley-Martin functional
response, Journal of Applied Mathematics and Computing (2013)
doi:10.1007/s12190-013-0674-0.
[13] X. Liu, S. Zhong, F. Zhong, Z. Liu, Properties of a stochastic predatorprey
system with Holling II functional response, Inter. J. Math. Sci., 2013,
7, 73-79.
[14] X. Li, X Mao. Population dynamical behavior of non-autonomous Lotka-
Volterra competitive system with random perturbation. Discrete Contin
Dyn Syst, 2009;24:523-545.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:66826", author = "Xianqing Liu and Shouming Zhong and Lijiang Xiang", title = "Asymptotic Properties of a Stochastic Predator-Prey Model with Bedding-DeAngelis Functional Response", abstract = "In this paper, a stochastic predator-prey system with Bedding-DeAngelis functional response is studied. By constructing a suitable Lyapunov founction, sufficient conditions for species to be stochastically permanent is established. Meanwhile, we show that the species will become extinct with probability one if the noise is sufficiently large.
", keywords = "Stochastically permanent, extinct, white noise,
Bedding-DeAngelis functional response.", volume = "8", number = "1", pages = "234-3", }
