| 具有时滞的食饵-捕食者模型的分支分析(英文) |
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| 引用本文： | 徐昌进,陈大学. 具有时滞的食饵-捕食者模型的分支分析(英文)[J]. 安徽大学学报(自然科学版), 2012, 0(1): 26-32 |
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| 作者姓名： | 徐昌进 陈大学 |
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| 作者单位： | 贵州财经学院贵州省经济系统仿真重点实验室数学与统计学院;湖南工程学院理学院 |
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| 基金项目： | Supported by National Natural Science Foundation of China(10771215);Scientific Research Fund of HunanProvincial Education Department(10C0560);Science and Technology Program of Hunan Province(2010FJ6021);ScientificResearch Initializing Foundation of Hunan Institute of Engineering(0744) |
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| 摘 要： | 研究一类具有时滞和比率依赖型功能反应函数的食饵-捕食者模型,通过局部和Hopf分支分析考察其动力学特性,分析其对应的特征方程,研究模型的线性稳定性和Hopf分支.同时得到了系统正平衡点稳定的时滞范围,给出数值模拟验证了所得结果的正确性.最后给出主要结论.
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| 关 键 词： | 食饵-捕食者模型 时滞 稳定性 Hopf分支 周期解 |
Bifurcation analysis in a delayed predator-prey model |
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| XU Chang-jin,CHEN Da-xue. Bifurcation analysis in a delayed predator-prey model[J]. Journal of Anhui University(Natural Sciences), 2012, 0(1): 26-32 |
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| Authors: | XU Chang-jin CHEN Da-xue |
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| Affiliation: | 1.Guizhou Key Laboratory of Economics System Simulation,School of Mathematics and Statistics,Guizhou College of Finance and Economics,Guiyang 550004,China;2.Faculty of Science,Hunan Institute of Engineering,Xiangtan 411004,China) |
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| Abstract: | In this paper,a delayed predator-prey model with ratio-dependent type functional response was considered.Its dynamics were studied in terms of local analysis and Hopf bifurcation analysis.By analyzing the associated characteristic transcendental equation,its linear stability was investigated and Hopf bifurcation was demonstrated.The length of delay which preserves the stability of the positive equilibrium was calculated.Some numerical simulations for justifying the analytical findings were also provided.Finally,main conclusions were given. |
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| Keywords: | predator-prey model time delay stability Hopf bifurcation periodic solution |
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