【作者】 刘洋；

【导师】 刘萍；

【作者基本信息】 哈尔滨师范大学 ， 应用数学， 2017， 硕士

【摘要】 偏微分方程理论来源于物理,化学,生态学和工程学等科学领域,具有强大的实际背景.捕食-食饵模型主要研究种群之间的相互作用,对保护生态方面有重要的意义.考虑到捕食者总会朝着食饵聚集的地方迁移并且捕食者和食饵自身的增长可以按照Logistic型增长,本文研究了一类具有食饵趋向性和Holling-II型的捕食食饵模型.首先,应用椭圆方程比较原理,得到任意非负解的有界性.然后给出唯一的共存解存在的参数范围,利用线性化方法分析了常数平衡解的局部稳定性;通过定义Lyapunov函数证明了常数平衡解的全局稳定性.最后应用全局分歧理论,证明系统从常数平衡解处发生的稳态分歧,得到了非常数解的存在性.更多还原

【Abstract】 The theory of partial differential equations is derived from the science of physic-s,chemistry,ecology,engineering and so on,with a strong practical background.The predator-prey model mainly studies the interaction between species,with im-portant significance for the protection of the ecological environment.Taking into account that the predator is always moving toward the prey,and the growth of the predator and the prey can follow the Logistic growth.In this paper,we have studied a kind of predator-prey model with prey-taxis and Holling-Ⅱ.Firstly,by using the comparison principle of elliptic equations,the boundedness of any nonnegative solution is obtained.Then we give the parameter range of the unique coexistence solution.And we analyse the local stability of the constant equilibria by the linearization methods;Furthermore,the global stability of the constant equilibrium is proved by using Lyapunov function.Finally,the existence of the non-constant solution and steady state bifurcation at constant equilibrium solution is proved by using the global bifurcation theory.更多还原