| 一类具有时滞的云杉蚜虫种群模型的Hopf分岔分析 |
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| 引用本文： | 曹建智,谭军,王培光.一类具有时滞的云杉蚜虫种群模型的Hopf分岔分析[J].应用数学和力学,2019,40(3):332-342. |
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| 作者姓名： | 曹建智 谭军 王培光 |
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| 作者单位： | 河北大学 数学与信息科学学院;河北省机器学习与计算智能重点实验室, 河北 保定 071002 |
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| 基金项目： | 国家自然科学基金(11771115)；河北省高等学校科学技术研究项目(QN2017018；QN2016030)；河北省自然科学基金(A2016201206) |
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| 摘 要： | 研究了一类具有时滞的云杉蚜虫种群阶段结构模型的动力学行为.首先，讨论了模型正平衡点的存在唯一性，并分析了该平衡点的局部稳定性和出现Hopf分岔的充分条件；其次，利用中心流形定理和正规形理论，讨论了分岔周期解的稳定性及方向；最后，通过数值模拟验证了相关结论的正确性.该文所得结论具有广泛的实际应用价值.
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| 关 键 词： | 云杉蚜虫种群模型 平衡点 稳定性 Hopf分岔 |
| 收稿时间： | 2018-04-08 |
Hopf Bifurcation Analysis of a Model for Spruce Budworm Populations With Delays |
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| Institution: | Key Laboratory of Machine Learning and Computational Intelligence of Hebei Province; College of Mathematics and Information Science, Hebei University, Baoding, Hebei 071002, P.R.China |
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| Abstract: | The dynamic behavior of a population model with stage structure for spruce budworms with time delay was investigated. Firstly, existence of a unique positive equilibrium of the model was discussed and sufficient conditions for local stability of the positive equilibrium and Hopf bifurcation occurrence were obtained. Next, the direction of the Hopf bifurcation and the stability of the periodic bifurcation solutions were analyzed with the normal form method combined with the center manifold theorem. Finally, some numerical simulations to verify the theoretical results were also conducted. The work provides an applicable reference for control of spruce budworms. |
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