一类单利相互竞争模型的分析

发布时间：2018-05-04 06:56

本文选题：偏利共生 + 相互竞争　；参考：《信阳师范学院》2015年硕士论文

【摘要】：在大自然中的无论哪个种群都要受到另一个种群的影响,然而大自然又是复杂的,有些物种之间不仅仅只存在单一的相互作用.例如,在一定养殖环境中的黑蚂蚁和蚜虫会为了争夺生存环境和资源而相互竞争,然而,蚜虫在竞争的过程中会产生蜜露,为黑蚂蚁的生长提供能量,对自己没有负影响,即两者之间又存在偏利共生的相互作用,也可以称为单利的相互作用.这种在特定环境下相互竞争时又单利的模型可以称为单利相互竞争模型.本文对单利相互竞争模型进行了分析.第一章介绍了本文的引言与预备知识.第二章首先介绍了没有时滞的单利相互竞争模型,然后根据现实情况建立了带有时滞的单利相互竞争模型,利用连续动力系统和时滞微分方程基本理论得到了该模型各个平衡点稳定性的条件.第三章首先建立了具有脉冲效应的单利相互竞争模型,然后利用脉冲微分方程系统的相关理论证明了此模型解的正性和有界性,并得到了这个系统持久性的充分条件.
[Abstract]:No matter which species in nature is affected by another population, however, nature is complex, some species not only exist a single interaction. For example, black ants and aphids in certain breeding environments will compete with each other for their living environment and resources. However, aphids will produce honeydew in the process of competition, which will provide energy for the growth of black ants and have no negative impact on themselves. That is, there is a symbiotic interaction between the two, also known as simple interest interaction. This kind of model with simple interest when competing with each other in a specific environment can be called the competition model of simple interest. This paper analyzes the competition model of simple interest. The first chapter introduces the introduction and preparatory knowledge of this paper. In the second chapter, we first introduce the model of simple interest competition without time delay, and then establish the model of simple interest competition with time delay according to the actual situation. By using the theory of continuous dynamical system and delay differential equation, the stability conditions of each equilibrium point of the model are obtained. In chapter 3, we first establish a simple interest competition model with impulsive effect, then we prove the positive and boundedness of the solution by using the theory of impulsive differential equation system, and obtain the sufficient condition for the persistence of the model.
【学位授予单位】：信阳师范学院
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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