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.

・我们已经研究了Lotka-Volterra两个物种系统，具有竞争关系，并在及时定期消失。在没有竞争关系的时期，两个物种种群中的每一个都彼此独立增长。我们的结果表明，竞争关系的暂时间歇性可能会导致哪种物种极端或两个物种共存的变化。有关此类特定阶段与模型中参数之间关系的结果已在某些国内或国际科学会议上进行了部分介绍，并计划在2002年在论文中发表。・我们已经研究了一些数学方法来分析Lotka-volterra Preyder predenter preadeator系统，并暂时间歇性灾难。 P.H.开发的方法Leslie（1958）以某种直观的方式扩展并应用于Lotka-Volterra Prey-Predator Ode System，我们可以从中衍生出的时间传输动态系统，从而保存原始ODE动态系统的特征。我们将扩展方法应用于数学生物学中其他基本数学模型的扩展方法，并表明那些派生的时间二散系统可以很好地保护原始系统的解决方案的行为。在一些国内和国际科学会议上已经提出了一些结果。・我们研究了Lotka-Volterra猎物predenter系统的收获术语，即暂时间歇性，也就是说，这是及时消失的。在具有暂时连续和谐的系统中，根据初始条件，猎物或捕食者的扩展在有限的时间内发生。相反，至于具有暂时间歇性和谐的系统，人口动态的结论可能会改变：例如，灭绝物种已改变。一些结果将在一些国内和国际科学会议上提出。