生境修复对具有Monod-Haldane功能反应的食饵捕食者系统的影响分析

张丽娟,庄需芹,赵宜宾,王福昌

系统科学与数学 ›› 2014, Vol. 34 ›› Issue (9) : 1138-1152.

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系统科学与数学 ›› 2014, Vol. 34 ›› Issue (9) : 1138-1152. DOI: 10.12341/jssms12409
论文

生境修复对具有Monod-Haldane功能反应的食饵捕食者系统的影响分析

    张丽娟,庄需芹,赵宜宾,王福昌
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DYNAMICAL COMPLEXITIES OF A MONOD-HALDANE TWO-PREY TWO PREDATOR SYSTEM WITH IMPULSIVE EFFECT AND HABITAT RESTORATION

    ZHANG Lijuan, ZHUANG Xuqin, ZHAO Yibin ,WANG Fuchag
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摘要

为研究生境修复对生态系统产生的影响, 文章建立了一类在生境破坏情况下, 具有~Monod-Haldane~功能反应, 脉冲比例收获和脉冲常数投放的四种群食饵--捕食者模型. 利用脉冲比较定理, Floquent~理论及微小扰动法研究了系统的动力学性质, 并给出系统中两食饵灭绝和种群持续生存的充分条件. 最后, 通过数值模拟验证了所得结论. 结果显示系统存在一定脆弱性和复杂性, 随着生境修复比率和捕食者投放比率的变化, 系统将出现拟周期, 混沌等复杂的动力学现象. 环境修复作用对系统影响的复杂性, 也体现了生境修复的重要性.

Abstract

In order to investigate the influence of habitat restoration on the ecological system, we have established a dynamical of a four-species prey-predator impulsive system with a Monod-Haldane function response, impulsive ration harvest and impulsive release. Basing on the strategy of integrated biology management, the frequent theorem and the amplitude perturbation skill, we give the sufficient conditions for the system of the preys to be extinct and permanence. Finally, we verified the conclusion by numerical simulation. The results showed some vulnerability and complexity. The system will have more complex dynamics including periodic doubling bifurcation, chaos, periodic halving bifurcation and so on with the change of the immigration and habitat restoration ratio. This also reflects the importance of habitat restoration.

关键词

生境修复 / 食饵捕食者 / 脉冲比较原理 / Floquent理论 / 混沌.

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张丽娟 , 庄需芹 , 赵宜宾 , 王福昌. 生境修复对具有Monod-Haldane功能反应的食饵捕食者系统的影响分析. 系统科学与数学, 2014, 34(9): 1138-1152. https://doi.org/10.12341/jssms12409
ZHANG Lijuan , ZHUANG Xuqin , ZHAO Yibin , WANG Fuchag. DYNAMICAL COMPLEXITIES OF A MONOD-HALDANE TWO-PREY TWO PREDATOR SYSTEM WITH IMPULSIVE EFFECT AND HABITAT RESTORATION. Journal of Systems Science and Mathematical Sciences, 2014, 34(9): 1138-1152 https://doi.org/10.12341/jssms12409
中图分类号: 35D35    34D23   
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