| 一类推广的Leslie-Gower型捕食-被捕食模型的动力学性质研究 |
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| 引用本文： | 刘华祥.一类推广的Leslie-Gower型捕食-被捕食模型的动力学性质研究[J].广东海洋大学学报,2009,29(3):53-58. |
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| 作者姓名： | 刘华祥 |
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| 作者单位： | 广东海洋大学理学院,广东湛江,524025 |
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| 基金项目： | 广东海洋大学科研资助项目 |
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| 摘 要： | 探讨了一类推广的Leslie-Gower型捕食-被捕食模型的动力学性质。以HollingII型功能反应和推广的Leslie-Gower模式为基础建立了无时滞和有时滞的捕食-被捕食种间作用模型;分析了无时滞模型共生平衡点的稳定性和Hopf分支,得到了共生平衡点的稳定性条件,找到了使系统发生Hopf分支的参数临界值,建立了系统存在稳定极限环的条件;分析了时滞模型系统共生平衡点的渐近稳定性以及孕育时滞参数值变化对模型系统共生平衡点稳定性的影响,找到了时滞模型系统发生Hopf分支的参数临界值,证明了当时滞参数在临界值附近变化时,系统也将发生Hopf分支。
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| 关 键 词： | Leslie-Gower型 Holling功能反应 捕食-被捕食 时滞 Hopf分支 |
Dynamical Properties Analysis of a Modified Leslie-Gower-type Prey-predator Model Systems |
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| LIU Hua-xiang.Dynamical Properties Analysis of a Modified Leslie-Gower-type Prey-predator Model Systems[J].Journal of Zhanjiang Ocean University,2009,29(3):53-58. |
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| Authors: | LIU Hua-xiang |
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| Abstract: | A two-dimensional modified Leslie-Gower-type prey-predator model system without and with discrete time-delay is explored. Basic dynamical properties of non-delayed and delayed model system in brief are discussed. Conditions for stability of the co-existing equilibrium point are obtained; The analysis on Hopf bifurcation is carried out; The existence of stable limit cycle of the non-delayed system is also established; We make local stability analysis of positive equilibrium point and Hopf-bifurcation analysis for the delayed model system by using Hopf-bifurcation theory and establish the existence of local Hopf-bifurcation as the time delay occurs around the threshold value.. |
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| Keywords: | Leslie-Gower type Holling functional reation prey-predaty time delay Hopf-bifurcation |
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