S~1上单种群模型研究
发布时间：2018-11-07 06:53
【摘要】：气候变迁影响生物种群赖以生存的栖息环境,为了适应这一变化,物种会跟随环境的变化而移动,其中候鸟就是一个典型的代表。本文首先以候鸟在一个环路上年复一年的迁徙现象为背景,在环形区域上建立了一个具有移动反应项的反应扩散方程模型;然后在适当的假设条件下,讨论模型正周期行波解的存在性。结果表明:环境移动速度的大小对正周期行波解的存在性有决定性影响。这对研究候鸟是否能够跟得上气候变迁是有积极意义的。文中首先将环形区域简化成圆环,并通过坐标变换,把相应的周期行波问题化简成平面系统的周期轨问题;然后利用相平面分析方法研究模型解的轨道性质,从而得到两个关于时间单调性的结果,进而用迭代的办法得到模型正周期行波解的存在性;最后,对在移动坐标下的反应扩散模型,进行了数值模拟,结果表明上述得到的正周期行波解是唯一且稳定的。
[Abstract]:In order to adapt to the climate change, species move with the change of environment, and migratory birds are a typical representative. In this paper, based on the migration of migratory birds on a ring road year after year, a reaction diffusion equation model with moving reaction term is established in the annular region. Then the existence of positive periodic traveling wave solutions is discussed under appropriate assumptions. The results show that the magnitude of environmental velocity has a decisive effect on the existence of positive periodic traveling wave solutions. This is positive for studying whether migratory birds can keep up with climate change. In this paper, the annular region is simplified into a circular ring, and the corresponding periodic traveling wave problem is reduced to the periodic orbit problem of the plane system by coordinate transformation. Then, the orbit property of the model solution is studied by using the phase plane analysis method, and two results about time monotonicity are obtained, and then the existence of the positive periodic traveling wave solution of the model is obtained by iterative method. Finally, a numerical simulation of the reaction diffusion model in moving coordinates is carried out. The results show that the positive periodic traveling wave solutions obtained above are unique and stable.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2315554
[Abstract]:In order to adapt to the climate change, species move with the change of environment, and migratory birds are a typical representative. In this paper, based on the migration of migratory birds on a ring road year after year, a reaction diffusion equation model with moving reaction term is established in the annular region. Then the existence of positive periodic traveling wave solutions is discussed under appropriate assumptions. The results show that the magnitude of environmental velocity has a decisive effect on the existence of positive periodic traveling wave solutions. This is positive for studying whether migratory birds can keep up with climate change. In this paper, the annular region is simplified into a circular ring, and the corresponding periodic traveling wave problem is reduced to the periodic orbit problem of the plane system by coordinate transformation. Then, the orbit property of the model solution is studied by using the phase plane analysis method, and two results about time monotonicity are obtained, and then the existence of the positive periodic traveling wave solution of the model is obtained by iterative method. Finally, a numerical simulation of the reaction diffusion model in moving coordinates is carried out. The results show that the positive periodic traveling wave solutions obtained above are unique and stable.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前3条
1 武红艳;;一类时滞反应扩散方程的行波解[J];晋中学院学报;2016年03期
2 潘雪军;董力强;;一类非线性方程的行波解分支[J];数学的实践与认识;2016年02期
3 马志军;;追踪鸟类的迁徙[J];科学;2013年01期
，本文编号：2315554
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