时间周期Lotka-Volterra捕食者—食饵系统的行波解与渐近传播速度
发布时间：2019-01-10 12:01
【摘要】：捕食者-食饵系统是一类经典的生物模型,它刻画了不同种群间的一种相互作用关系.对该系统行波解和渐近传播速度的深入研究,可以解释和预测自然界中的某些生物现象,因此它在过去的几十年里被广泛地关注.但这其中大多数的结果只考虑了带有常系数的反应扩散系统的行波解以及渐近传播,而具有时间周期的系统的相关结果却很少.因此,本文将主要研究带有时间周期的Lotka-Volterra捕食者-食饵反应扩散系统的行波解和渐近传播速度.本文首先研究了该系统的周期行波解的存在性和渐近行为.先构造一组合适的上下解从而得到一个由周期函数构成的非空闭凸集,然后在此集上定义非线性算子,再利用Schauder不动点定理得到非平凡周期行波解的存在性.还结合渐近传播理论和全局渐近稳定周期解的一些收敛结果,给出了行波解的渐近行为.此外,根据比较原理和渐近传播理论,建立了行波解的不存在性.最后在两种不同的假设条件下讨论了该系统的渐近传播速度,其基本方法是利用渐近传播理论,并结合辅助方程和比较原理.情形一,捕食者在共同入侵栖息地过程中占优势时,本文得到了捕食者的传播速度和食饵传播速度的上下界.结果表明捕食者的传播速度可以不受种群间相互作用的影响,而食饵的传播速度会减慢,也就是捕食者对食饵的种群的发展起负作用.情形二,当食饵入侵占优势时,文中得到了食饵的传播速度和捕食者传播速度的一个下界.结果表明种群间的相互作用可以不改变食饵的传播速度,却会加快捕食者的传播速度,即食饵能促进捕食者种群的发展.
[Abstract]:Predator-prey system is a classical biological model, which describes the interaction between different populations. The study of traveling wave solution and asymptotic propagation velocity of this system can explain and predict some biological phenomena in nature, so it has been paid more and more attention in the past few decades. However, most of the results only consider the traveling wave solution and asymptotic propagation of the reaction diffusion system with constant coefficients, but the correlation results of the system with time period are few. Therefore, the traveling wave solution and asymptotic propagation velocity of Lotka-Volterra predator-prey reaction diffusion system with time period will be studied in this paper. In this paper, the existence and asymptotic behavior of periodic traveling wave solutions for the system are studied. A set of suitable upper and lower solutions is constructed to obtain a nonempty closed convex set composed of periodic functions. Then nonlinear operators are defined on the set, and then the existence of nontrivial periodic traveling wave solutions is obtained by using Schauder fixed point theorem. The asymptotic behavior of traveling wave solutions is also given by combining the asymptotic propagation theory and some convergence results of globally asymptotically stable periodic solutions. In addition, according to the comparison principle and asymptotic propagation theory, the nonexistence of traveling wave solution is established. Finally, the asymptotic propagation velocity of the system is discussed under two different assumptions. The basic method is to use the asymptotic propagation theory, combined with the auxiliary equation and the principle of comparison. In the first case, when the predator is dominant in the process of invading the habitat together, the upper and lower bounds of the predator's propagation speed and the prey's propagation speed are obtained in this paper. The results show that the propagating speed of predator can not be affected by the interaction between populations, but the propagation speed of prey will slow down, that is, the predator plays a negative role in the development of prey population. In the second case, when the prey invasion is dominant, a lower bound of the propagation speed of prey and predator is obtained. The results show that the interaction between populations can not change the propagation speed of prey, but accelerate the spread of predator, that is, prey can promote the development of predator population.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2406282
[Abstract]:Predator-prey system is a classical biological model, which describes the interaction between different populations. The study of traveling wave solution and asymptotic propagation velocity of this system can explain and predict some biological phenomena in nature, so it has been paid more and more attention in the past few decades. However, most of the results only consider the traveling wave solution and asymptotic propagation of the reaction diffusion system with constant coefficients, but the correlation results of the system with time period are few. Therefore, the traveling wave solution and asymptotic propagation velocity of Lotka-Volterra predator-prey reaction diffusion system with time period will be studied in this paper. In this paper, the existence and asymptotic behavior of periodic traveling wave solutions for the system are studied. A set of suitable upper and lower solutions is constructed to obtain a nonempty closed convex set composed of periodic functions. Then nonlinear operators are defined on the set, and then the existence of nontrivial periodic traveling wave solutions is obtained by using Schauder fixed point theorem. The asymptotic behavior of traveling wave solutions is also given by combining the asymptotic propagation theory and some convergence results of globally asymptotically stable periodic solutions. In addition, according to the comparison principle and asymptotic propagation theory, the nonexistence of traveling wave solution is established. Finally, the asymptotic propagation velocity of the system is discussed under two different assumptions. The basic method is to use the asymptotic propagation theory, combined with the auxiliary equation and the principle of comparison. In the first case, when the predator is dominant in the process of invading the habitat together, the upper and lower bounds of the predator's propagation speed and the prey's propagation speed are obtained in this paper. The results show that the propagating speed of predator can not be affected by the interaction between populations, but the propagation speed of prey will slow down, that is, the predator plays a negative role in the development of prey population. In the second case, when the prey invasion is dominant, a lower bound of the propagation speed of prey and predator is obtained. The results show that the interaction between populations can not change the propagation speed of prey, but accelerate the spread of predator, that is, prey can promote the development of predator population.
【学位授予单位】：兰州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关硕士学位论文 前1条
1 薄伟健;周期弱竞争Lotka-Volterra系统的行波解和渐近传播[D];兰州大学;2016年
，本文编号：2406282
本文链接：https://www.wllwen.com/kejilunwen/yysx/2406282.html
