Mathematical Modelling Analysis for Population Dynamics with Temporally Intermittent Specific Interaction

我们研究了一个Lotka-Volterra两种物种系统，这种系统具有竞争力的关系在时间上逐渐消失。在没有竞争关系的情况下，两种物种的每种种群都独立地生长在彼此之间。我们的结果表明，竞争关系的这种暂时暂时性可能导致任何物种的变化发生更长的时间或两种物种的共存。关于在模型中这样一个特定阶段和参数之间的关系的结果，已在一些领域或国际科学会议上提出，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 Pre-predator系统与临时间歇干扰。由P.H.开发的方法Leslie （1958年）在Lotka-Volterra Pre-predator ODE系统中的一些直觉方法已经扩展和应用，我们可以将时间离散的动态系统从它衍生出来，从而保护原始ODE动态系统的特征。我们已经为数学生物学中的其他基本数学模型应用了我们的扩展方法，并展示那些衍生出来的离散时间系统可以保存良好的解决方案行为来解决原始系统。一些结果已经在一些家庭和国际科学会议上提出了。我们已经研究了一个带有Lotka-Volterra predator系统的收获期，什么是暂时的，什么是暂时消失的周期性的。在一个具有临时连续收获的系统中，捕食者或捕食者在有限时间内的扩展，依赖于初始条件。在对比下，由于该系统与临时临时间歇收获，人口动力学的融合可以改变：由于实例，更广泛的物种也会改变。一些结果将在一些家庭和国际科学会议上提出。

・ 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.