Dynamical analysis on stochastic three-specy model with impusive toxicant

Abstract

Abstract: A stochastic three-specy prey-predator model with Beddington-DeAngelis functional response and impusive toxicant input is studied in order to find out how white noise and impusive toxicant input influence the dynamics of the model. By analyzing the limit system of the proposed model, the sufficient conditions for extinction, mean strong persistence and superior bound with average time are supplied.

Key words: three-specy model, impluse, extinction, mean strong persistence, white noise

CLC Number:

O175.6

GAO Yongxin, WANG Nana. Dynamical analysis on stochastic three-specy model with impusive toxicant[J]. Journal of Civil Aviation University of China, 2020, 38(3): 61-64.

References 12

[1]	HALLAM T G, CLARK C E, LASSITER R R. Effects of toxicants on populations: a qualitative approach I. Equilibrium environmental exposure[J]. Ecological Modelling, 1983, 18(3/4): 291-304.
[2]	AGARWAL M, DEVI S. The effect of environmental tax on the survival of biological species in a polluted environment: a mathematical model[J]. Nonlinear Analysis Modelling & Control, 2010, 3(3): 15-24.
[3]	WEN XIANZHANG, WANG ZHICHENG. Persistence and extinction in two species models with impulse[J]. Acta Mathematica Sinica(English Series), 2006, 2: 447-454.
[4]	LIU MENG, ZHANG LEI. Dynamics of a two-species Lotka-Volterra competition system in a polluted environment with pulse toxicant input[J]. Applied Mathematics and Computation, 2009, 214(1): 155-162.
[5]	BAHAR A, MAO X. Stochastic delay Lotka-Volterra model[J]. Journal of Mathematical Analysis & Applications, 2004, 292(2): 364-380.
[6]	LIU MENG, WANG KE. Persistence, extinction and global asymptotical stability of a non-autonom ous predator-prey model with random perturbation[J]. Applied Mathematical Modelling, 2012, 36: 5344-5353.
[7]	LIU MENG, WANG KE. Stochastic Lotka-Volterra systems with L佴vy noise[J]. Journal of Mathematical Analysis & Applications,2014, 410(2):750- 763.
[8]	LIU QUN, CHEN QINGMEI, LIU ZHENHAI. Analysis on stochastic delay Lotka-Volterra systems driven by L佴vy noise[J]. Applied Mathematics & Computation, 2014, 235: 261-271.
[9]	BAI LING, LI JINGSHI, ZHANG KAI, et al. Analysis of a stochastic ratio-dependent predator-prey model driven by L佴vy noise[J]. Applied Mathematics & Computation, 2014, 233(1): 480-493.
[10]	董冉冉, 张道祥, 尹红云. 一类带Beddington -DeAngelis 功能反应的基于比率依赖的三种群扩散捕食者-食饵系统的周期解[J]. 生物数学学报, 2012, 27(2): 213-223.
[11]	LIU MENG, WANG KE, WU QIONG. Survival analysis of stochastic competitive models in a polluted environment and stochastic competitive exclusion principle[J]. Bulletin of Mathematical Biology, 2011, 73:1969-2012.
[12]	ZHANG TONGQIAN, MA WANBIAO, MENG XINZHU. Global dynamics of a delayed chemostat model with harvest by impulsive flocculant input[J]. Advances in Difference Equations, 2017, 1: 1-17.