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| 具时滞和扩散单种群模型的一致持续生存与全局稳定性 | |
| 引用本文： | 邢铁军,雒志学,杜明银,王武民. 具时滞和扩散单种群模型的一致持续生存与全局稳定性[J]. 数学的实践与认识, 2012, 42(6): 180-185 |
| 作者姓名： | 邢铁军 雒志学 杜明银 王武民 |
| 作者单位： | 1. 甘肃省酒泉中学,甘肃酒泉,735000 2. 兰州交通大学数理与软件工程学院,甘肃兰州,730070 3. 河南理工大学万方科技学院(郑州校区),河南郑州,451400 4. 呼和浩特铁路局,内蒙古呼和浩特,010057 |
| 摘 要： | 讨论了一类具有时滞的单种群扩散模型,其中扩散依赖于时滞,利用同伦技术得到了模型存在正平衡点和系统一致持续生存的充分条件;同时通过构造适当的liapunov函数证明了系统正平衡点是全局渐渐稳定的. |
| 关 键 词： | 时滞 扩散 一致持续生存 同伦技术 全局渐进稳定性 |
Permanence and Global Stability for Single Species Model with Time Delay and Diffusion |
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| XING Tie-jun , LUO Zhi-xue , DU Ming-yin , WAMG Wu-min. Permanence and Global Stability for Single Species Model with Time Delay and Diffusion[J]. Mathematics in Practice and Theory, 2012, 42(6): 180-185 | |
| Authors: | XING Tie-jun LUO Zhi-xue DU Ming-yin WAMG Wu-min |
| Affiliation: | XING Tie-jun1,LUO Zhi-xue2,DU Ming-yin3,WAMG Wu-min4 (1.Jiuquan Middle School of Gansu Province,Jiuquan 735000,China) (2.College of Mathematics,Physics Software Engineering,Lanzhou Jiaotong University,Lanzhou 730070, China) (3.Wanfang Institute of Science and Technology Henan Polytechnic University,Zhengzhou 451400,China) (4.The Department of Transportion of Huhehaote,Huhehaote 010057,China) |
| Abstract: | In this paper,a single-species with time delays and diffusion is investigated, where diffusions depended on constant time delay.It has a positive equilibrium by homotopy techniques.The sufficient conditions for the permanence of the system are obtained.Asol,by using appropriate Liapunov function,we proved the positive equilibrium is global asymptotic stability. |
| Keywords: | time delay diffusion homotopy techniques permanence global asymptotic stability |
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