Asymptotic behavior of a non-autonomous predator-prey model with Hassell–Varley type functional response and random perturbation

被引：5

作者：

Zhang Y. ^{[1
]}

Gao S. ^{[1
]}

Fan K. ^{[2
]}

Wang Q. ^{[1
]}

机构：

[1] Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou

[2] School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou

来源：

Journal of Applied Mathematics and Computing | 2015年 / 49卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Non-autonomous model; Persistence; Stochastic disturbance;

D O I：

10.1007/s12190-014-0854-6

中图分类号：

学科分类号：

摘要：

This paper considers a new non-autonomous predator-prey model with stochastic perturbation and Hassell–Varley type functional response. Based on classical comparison theorem of stochastic equations, (Formula Presented.) formula and skillful analysis techniques, the existence of a global positive solution and stochastically ultimate boundedness are derived. Furthermore, some sufficient and necessary criteria for extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and the global attractivity of the system are obtained. At last, a series of numerical simulations to illustrate our mathematical findings are presented and some conclusions are also given. © 2014, Korean Society for Computational and Applied Mathematics.

引用

页码：573 / 594

页数：21

共 33 条

[1]

Berryman A.A., The origins and evolution of predator-prey theory, Ecology, 73, pp. 1530-1535, (1992)

[2]

Kuang Y., Beretta E., Global qualitative analysis of a ratio-dependent predator-prey system, J. Math. Biol., 36, pp. 389-406, (1998)

[3]

Zhou X.Y., Cui J.A., Shi X.Y., Song X.Y., A modified Leslie–Gower predator-prey model with prey infection, J. Appl. Math. Comput., 33, pp. 471-487, (2010)

[4]

Liu X.Q., Zhong S., Tian B.D., Zheng F.X., Asymptotic properties of a stochastic predator-prey model with Crowley–Martin functional response, J. Appl. Math. Comput., 43, pp. 479-490, (2013)

[5]

Zhang Y., Gao S.J., Liu Y.J., Analysis of a nonautonomous model for migratory birds with saturation incidence rate, Commun. Nonlinear Sci. Numer. Simul., 17, pp. 1659-1672, (2012)

[6]

Chen Y., Liu Z.J., Haque M., Analysis of a Leslie–Gower-type prey-predator model with periodic impulsive perturbations, Commun. Nonlinear Sci. Numer. Simul., 14, pp. 3412-3423, (2009)

[7]

Arditi R., Perrin N., Saiah H., Functional responses and heterogeneities: an experimental test with cladocerans, OIKOS, 60, pp. 69-75, (1991)

[8]

Arditi R., Saiah H., Empirical evidence of the role of heterogeneity in ratio-dependent consumption, Ecology, 73, pp. 1544-1551, (1992)

[9]

Gutierrez A.P., The physiological basis of ratio-dependent predator-prey theory: a metabolic pool model of Nicholson’s blowflies as an example, Ecology, 73, pp. 1552-1563, (1992)

[10]

Wang K., Zhu Y.L., Pernamence and global asymptotic stability of a delayed predator-prey model with Hassell–Varley type functional response, Bull. Iran. Math. Soc., 37, 3, pp. 197-215, (2011)

← 1 2 3 4 →