| 一类具有比例和常数脉冲收获的周期竞争系统周期解的存在性 |
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| 引用本文： | 卢拉拉,窦家维. 一类具有比例和常数脉冲收获的周期竞争系统周期解的存在性[J]. 山东大学学报(理学版), 2012, 47(9): 98-104,115 |
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| 作者姓名： | 卢拉拉 窦家维 |
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| 作者单位： | 陕两师范大学数学与信息科学学院,陕西西安,710062 |
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| 基金项目： | 国家自然科学基金资助项目(10971124,61070189) |
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| 摘 要： | 研究了一类周期环境中既有比例收获又有常量收获的一维脉冲系统正周期解存在的条件以及解的一些基本性质;以此为基础构造一个迭代格式,利用单调迭代方法证明了二维Lotka-Volterra竞争系统正周期解的存在定理,得到了保证系统正周期解存在的一组容易验证的充分条件。该方法是构造性的,以利于用数值方法求其周期解。给出一个实例并用数值模拟方法解释说明了所获得的主要结论。
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| 关 键 词： | Lotka-Volterra竞争系统 比例及常量脉冲收获 单调迭代方法 周期解 |
The periodic solution for a class of competition system with proportional and constant impulse harvesting |
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| LU La-la,DOU Jia-wei. The periodic solution for a class of competition system with proportional and constant impulse harvesting[J]. Journal of Shandong University, 2012, 47(9): 98-104,115 |
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| Authors: | LU La-la DOU Jia-wei |
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| Affiliation: | (College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,Shaanxi,China) |
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| Abstract: | The existence of the positive periodic solution was studied for a class of periodic logistic equation with impulsive harvesting,which includes both cases of the proportional and constant harvesting.Then,based on the results obtained for logistic equation,a monotone-iterative scheme was established to obtain the existence of the positive periodic solutions for Lotka-Volterra competition system.This method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic solution.An example was given and some computer simulations were carried out to demonstrate the main results. |
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| Keywords: | Lotka-Volterra competition system proportional and constant impulse harvesting monotone-iterative method periodic solution |
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