| 基于比率的两种群捕食者-食饵系统的周期解 |
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| 引用本文： | 董士杰,朱玉峻,郭彦平.基于比率的两种群捕食者-食饵系统的周期解[J].河北科技大学学报,2004,25(1):1-5. |
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| 作者姓名： | 董士杰 朱玉峻 郭彦平 |
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| 作者单位： | 军械工程学院基础部,河北,石家庄,050003;河北师范大学数学与信息学院,河北,石家庄,050016;河北科技大学理学院,河北,石家庄,050018 |
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| 基金项目： | 河北省自然科学基金资助项目(603384) |
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| 摘 要： | 对于捕食者 食饵系统已有大量的研究工作,主要集中于解的稳定性、持久性等,关于周期性结论很少。本文研究了一类非自治的具有时滞和基于比率且有Machaelis Menten型功能性反应的两种群捕食者 食饵周期系统 x1=x1(t)(a(t)-b(t)x1(t)-c(t)x1(t)x2(t)m(t)x22(t)+x21(t)), x2=x2(t)(-d(t)+e(t)x21(t-τ)m(t)x22(t-τ)+x21(t-τ)),利用Mawhin的重合度理论和不等式技巧,找到了系统的1个先验界,并建立了这类系统正周期解的存在性判据。
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| 关 键 词： | 捕食者-食饵系统 正周期解 重合度理论 |
| 文章编号： | 1008-1542(2004)01-0001-04 |
| 修稿时间： | 2003年5月1日 |
Periodic Solutions of a Ratio-dependent Predator-prey System of Tow Species |
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| DONG Shi-jie,ZHU Yu-jun,GUO Yan-ping.Periodic Solutions of a Ratio-dependent Predator-prey System of Tow Species[J].Journal of Hebei University of Science and Technology,2004,25(1):1-5. |
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| Authors: | DONG Shi-jie ZHU Yu-jun GUO Yan-ping |
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| Institution: | DONG Shi-jie~1,ZHU Yu-jun~2,GUO Yan-ping~3 |
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| Abstract: | For the predator-prey most work of study focuses on the stability and persistence while there have ever been little results about the periodicity.In this paper,we study a two-species ratio-dependent predator-prey system with time delay and Machaelis-menten type functional response _1=x_1(t)(a(t)-b(t)x_1(t)-c(t)x_1(t)x_2(t)m(t)x~2_2(t) x~2_1(t)), x_2=x_2(t)(-d(t) e(t)x~2_1(t-r)m(t)x~2_2(t-r) x~2_1(t-r)). By using Mawhin's coincidence degree thoery and technique of inequalities,we obtain a prior boundary of the system,and establish the existence result of positive periodic solution for the system. |
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| Keywords: | predator-prey system positive periodic solution coincidence degree theory |
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