| 具有时滞和避难所的复合型竞争合作模型的Hopf分支 |
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| 引用本文： | 周青娇,魏凤英.具有时滞和避难所的复合型竞争合作模型的Hopf分支[J].福州大学学报(自然科学版),2016,44(3):320-324. |
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| 作者姓名： | 周青娇 魏凤英 |
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| 作者单位： | 福州大学数学与计算机科学学院 福建 福州350116,福州大学数学与计算机科学学院 福建 福州350116 |
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| 基金项目： | 国家自然科学基金资助项目(11201075)；福建省自然科学基金资助项目(2010J01005) |
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| 摘 要： | 考虑一类具有时滞及避难所的复合型竞争合作模型的Hopf分支情况,通过分析雅克比矩阵的特征值证明当时滞τ在一定范围内变化时,正平衡点是局部渐近稳定的.当时滞τ穿过某些特定值时,该模型在正平衡点附近产生Hopf分支.最后,通过数值模拟验证所得结论的有效性.
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| 关 键 词： | 复合型竞争合作系统 避难所 时滞 Hopf分支 |
| 收稿时间： | 1/5/2014 12:00:00 AM |
Hopf bifurcation of a mixed cooperation-competition model incorporating time delay and refuge |
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| ZHOU Qingjiao and WEI Fengying.Hopf bifurcation of a mixed cooperation-competition model incorporating time delay and refuge[J].Journal of Fuzhou University(Natural Science Edition),2016,44(3):320-324. |
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| Authors: | ZHOU Qingjiao and WEI Fengying |
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| Institution: | College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, Fujian and College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, Fujian |
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| Abstract: | The Hopf bifurcation of a mixed cooperation-competition model incorporating time delay and refuge is considered in this paper. By analyzing the eigenvalues of Jacobian matrices, the sufficient condition of the local asymptotical stability of the positive equilibrium is obtained and when tau passes through some special value, Hopf bifurcations occur at the positive equilibrium of the model. Numerical simulations are carried out to illustrate the effectiveness of our results. |
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| Keywords: | Mixed cooperation-competition model Refuge Time delay Hopf bifurcation |
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