【摘要】：氣候變遷影響生物種群賴以生存的棲息環(huán)境,為了適應(yīng)這一變化,物種會跟隨環(huán)境的變化而移動,其中候鳥就是一個典型的代表。本文首先以候鳥在一個環(huán)路上年復(fù)一年的遷徙現(xiàn)象為背景,在環(huán)形區(qū)域上建立了一個具有移動反應(yīng)項(xiàng)的反應(yīng)擴(kuò)散方程模型;然后在適當(dāng)?shù)募僭O(shè)條件下,討論模型正周期行波解的存在性。結(jié)果表明:環(huán)境移動速度的大小對正周期行波解的存在性有決定性影響。這對研究候鳥是否能夠跟得上氣候變遷是有積極意義的。文中首先將環(huán)形區(qū)域簡化成圓環(huán),并通過坐標(biāo)變換,把相應(yīng)的周期行波問題化簡成平面系統(tǒng)的周期軌問題;然后利用相平面分析方法研究模型解的軌道性質(zhì),從而得到兩個關(guān)于時間單調(diào)性的結(jié)果,進(jìn)而用迭代的辦法得到模型正周期行波解的存在性;最后,對在移動坐標(biāo)下的反應(yīng)擴(kuò)散模型,進(jìn)行了數(shù)值模擬,結(jié)果表明上述得到的正周期行波解是唯一且穩(wěn)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.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：2315554