一类具有相互干扰的捕食—食饵系统的定性分析

【作者】 李军；

【导师】 蒋勇；

【作者基本信息】 南京理工大学 ， 计算数学， 2010， 硕士

【摘要】 种群生态学中生物体与环境以及生物群体间的关系,可以用动力学的观点来揭示。捕食-食饵动力学模型可以有效地描述、预测以至调节和控制物种的发展过程和发展趋势,是种群生态学和生物数学研究的热点。传统的捕食-食饵模型主要针对捕食与被捕食关系和捕食者种群内部的相互干扰,但当生态系统中存在多个捕食者种群时,这些捕食者之间的种间干扰对生态系统的发展起着不容忽视的作用,是构造动力学模型时应该加以考虑的重要因素。本文在文献[35]的基础上构造了一类关于非单调Ⅳ类功能反应、非线性密度制约且具有相互干扰的三种群捕食-食饵模型,论文的第一章介绍了问题研究的背景及意义、已有的研究成果、本文的主要工作和预备知识；第二章采用微分方程定性和稳定性理论的方法分析了系统平衡点的局部、全局稳定性；第三章给出了三种群持久生存的充分条件,另外当模型参数变化时,讨论了系统的Hopf分支；并对所得定理做了数值模拟,以验证理论推导的正确性。结论表明三种群相互作用会导致一个捕食者种群灭亡,而另外两个种群趋于正平衡态或以周期振荡的形式共存,或者两个捕食者种群都灭亡,或者三个种群都持久共存。更多还原

【Abstract】 In population ecology the interaction among species and the relationship between environment and species can be revealed from the viewpoint of dynamics. Predator-prey dynamical system which is a hot topic in filed of mathematical biology and population ecology can describe、predict and control the development of species.Traditional predator-prey model mainly focus on predator-prey relationship and intraspecific mutual interference of predators. However, if there exist more than one predator specie in the ecological system, the interspecies interference among them plays an important role during the evolution of ecological system, which can not be ignored when we establish the dynamical model.Based on the document [35], three species of predator-prey model involving non-monotonic functional response, nonlinear density dependence and interspecies mutual interference is created. In the first chapter, we introduce the background and research significance of problems which will be investigated as well as main work of this paper. At same time the review of existing research results, together with some basic theory concerning the qualitative theory and stability theory of ordinary differential equation are given. In the second chapter, local and global stability of equilibrium is analyzed by using qualitative analysis and stability theory of ordinary differential equation. In the third chapter the sufficient conditions of permanence are obtained and the Hopf bifurcation of system is studied when the parameters of model change. Moreover theoretical analyses are verified by numerical simulation. The finding shows that the interaction among three species may cause one of predator species becomes extinct, the other two species coexist in the form of positive equilibrium state or periodic oscillation; or both of them become extinct; or all three species tend to permanent state.更多还原