【作者】 芦雪娟；

【导师】 李冬梅；

【作者基本信息】 哈尔滨理工大学 ， 基础数学， 2006， 硕士

【摘要】 通过对具有收获率的捕食与被捕食系统的定性分析,可以预测种群的发展变化趋势,及人们的捕获行为对种群的影响,并判断付出多大的捕获努力量,既可维持生态系统的平衡,又能使收获量达到最大来满足人类的需要。故对具有收获率的捕食与被捕食系统的研究,将对可更新资源进行合理的开发与利用问题起指导作用,直接关系到资源的可持续发展问题,其意义尤为重要。目前对于同时具有常数收获率的捕食与被捕食系统的研究甚少,故本文是在已有结果基础上,对同时具有常数收获率的捕食系统平衡点的性态作了进一步研究。首先讨论了食饵种群在线性密度制约下的一类HollingⅡ、Ⅲ类功能性反应模型。利用定性分析的方法,借助等倾线函数的性质,绘制出等倾线图象,得到了模型在具有常数收获率的条件下,平衡点的存在条件、解的有界性、闭轨的不存在条件以及平衡点的定性问题。对同时具有常数收获率的一般性功能反应模型,利用上述定性分析的方法,给出了正平衡点的稳定性、解的有界性、闭轨不存在的条件。对于同时具有常数收获率的Kolmogorov模型。以一类Kolmogorov模型出发,借助定性分析方法及等倾线对应方程的根与系数的关系,绘制出等倾线图象的变化趋势,判断出平衡点的存在,从而给出平衡点的存在条件;用Bendixson环域定理证明了闭轨的不存在性;再借助线性变换将模型转化为标准型,利用焦点量的计算结果给出了极限环存在条件。对于一般性的Kolmogorov模型,给出了平衡点的存在条件,确定了平衡点的稳定性,讨论了闭轨的不存在性。更多还原

【Abstract】 With studying the predator-prey system with harvesting rate by qualitative analysis, it predicts the development and change of population and to analyze the capture behaviors effect on the population. We can decide how much capture quantity is to maintain the balance of ecological system and to satisfy the need, when capture quantity reaches the top. From these facts, it is very important that the system with harvesting rate relates to the problem of resource continuable development, because it guides to renew the resources to carry on reasonable of exploitation and utility.At present, to the research of predator-prey system with constant harvesting rate simultaneity study little, on the basis of work which has been done, therefore this paper makes further study on the equilibrium point of predator-prey system with constant harvesting rate. Firstly, it discusses a class of predator-prey system with HollingⅡ、Ⅲfunctional response in linear dense restrict prey system. With using general qualitative analysis methods, and in virtue of the function property of the isoclinic line, it protracts the image of the isoclinic line, and gets the conditions of existence of equilibrium point and the boundary property of the solution, and the conditions of inexistence of the close curve and the qualitative of the equilibrium point in the conditions of prey-predator system with constant harvesting rate. To the general functional response model with constant harvesting rate simultaneity, it gets the stability of the equilibrium point and the boundary property of the solution and the conditions of inexistence of close curve with utilizing qualitative analysis methods.Concerning Kolmogorov model of constant harvesting rate simultaneity, this paper still sets out a class of Kolmogorov model, in virtue of qualitative analysis methods and the relation of the root and coefficient of the corresponding equation of the isoclinic line, portracts the trend of the isoclinic line, judge the更多还原