Mathematical Modelling Analysis for Population Dynamics with Temporally Intermittent Specific Interaction

具有时间间歇特定相互作用的种群动态数学模型分析

基本信息

批准号：
12640126
负责人：
SENO Hiromi
金额：
$ 1.54万
依托单位：
Hiroshima University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2001
项目状态：
已结题

项目摘要

・ We have studied the Lotka-Volterra two species system with competitive relationship which is disappeared periodically in time. In the period without competitive relationship, each of two species populations grows independently of each other. Our results show that such temporally intermittency of competitive relationship can cause the change of which species goes extince or the coexistence of two species. Results about the relation between such specific phases and the parameters in model have been presented in part at some domestic or international scientific meetings, and are planned to be published in paper in 2002.・ We have studied some mathematical methods to analyze the Lotka-Volterra prey-predator system with temporally intermittent disturbance. Method developed by P.H. Leslie (1958) in some intuitive way is extended and applied for Lotka-Volterra prey-predator ODE system, and we can obatin a time-discrete dynamical system derived from it, which conserves the characteristics of original ODE dynamical system. We applied our extended method for the other fundamental mathematical models in Mathematical Biology, and show that those derived time-discrete systems can conserve well the behavior of solution for the original system. Some results have been already presented in some domestic and international scientific meetings.・ We have studied the Lotka-Volterra prey-predator system with harvestion term which is temporally intermittent, that is, which is disappeared periodically in time. In the system with temporally continuous harvestion, the extinction of prey or predator occurs in a finite time, depending on the initial condition. In contrast, as for the system with temporally intermittent harvestion, the conclusion of population dynamics can change : for instance, the extinct species is changed. Some results will be presented in some domestic and international scientific meetings.

・我们研究了具有竞争关系的Lotka-Volterra 两个物种系统，在没有竞争关系的时期，两个物种种群各自独立生长。我们的结果表明，这种竞争关系的时间间歇性可以实现。导致哪个物种灭绝或两个物种共存的具体阶段与模型参数之间关系的结果已在一些国内或国际科学会议上发表，并计划在论文中发表。 2002.・我们研究了一些数学方法来分析具有时间间歇性扰动的 Lotka-Volterra 捕食者系统。 P.H. Leslie (1958) 开发的方法以某种直观的方式扩展并应用于 Lotka-Volterra 捕食者-捕食者 ODE 系统，由此我们可以得到一个时间离散动力系统，它保留了原始ODE动力系统的特征，我们将我们的扩展方法应用于其他基本数学模型。数学生物学，并表明所导出的时间离散系统可以很好地保留原始系统的解的行为，我们已经在一些国内和国际科学会议上提出了一些结果。具有时间间歇性的收获项，即在时间上周期性消失的系统中，猎物或捕食者的灭绝发生在有限的时间内，具体取决于初始条件。系统随着时间的间歇性收获，种群动态的结论可能会发生变化：例如，灭绝的物种会发生变化，一些结果将在一些国内和国际科学会议上提出。