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| A predator-prey system model with Holling II functional response and Allee effect |
| JIANG Rui1, LIU Hua1, XIE Mei1, WEI Yu-mei2, ZHAO Shifeng1 |
1. School of mathematics and computer science Institute ,Northwest university for nationalities, Lanzhou 730030, China
2. The experiment center, Northwest university for nationalities, Lanzhou 730030, China |
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Abstract This paper studied the dynamic complexity of a class of discrete population model by computer simulation. The autonomous predator-prey system model is established through theoretical derivation, which has Allee effect and Holling II functional effect. The growth states of discrete-time populations are simulated to explore the influence of the parameters’changes to its population size by MATLAB. It also illustrated the importance of Allee effect and Holling II functional in the model of interaction among populations. The research results show that the larger the processing time, the bigger parameter region for stable coexistence population when the processing time is within the effective range. The introduction of Allee effect makes dynamic behavior of the population more complicated, thus increase the extinction risk of predator population. The population appears bifurcation in advance when predator-prey system strongly affected by Allee effect. It will lead to population extinction, if Allee effect increasingly raises. The strong Allee effect is more prone to population extinction. The conclusion of this paper not only enriches the theory of ecology, but also puts forward important basis of conservation ecology.
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Received: 13 November 2015
Published: 16 May 2018
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具有Holling Ⅱ型功能反应和Allee效应的捕食系统模型
利用计算机模拟方法研究一类离散种群相互作用模型的动态复杂性. 通过理论推导建立食饵具有Allee效应和HollingⅡ型功能反应的自治捕食系统模型,用Matlab软件模拟离散种群的生长状态, 探索研究参数的变化对种群大小的影响, 阐释Allee效应及HollingⅡ型功能反应在种群间相互作用模型中的重要性. 研究结果表明: 1)当处理时间处于有效区间内时, 处理时间越大种群的稳定共存参数域越大; 2)Allee效应的引入使种群的动态行为更为复杂, 从而增加了捕食者种群的灭绝风险; 3)系统受强Allee效应的影响, 种群会出现提前分叉现象, 如果继续增加Allee效应就会导致种群灭绝; 4)强Allee效应更容易使种群趋向灭绝. 所得结论在丰富生态学理论的同时, 提出了保护生态学的重要依据.
关键词：
Allee效应,
HollingⅡ型,
混沌,
计算机模拟
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