本文選題：Leslie-Gower系統(tǒng) + 行波解��； 參考：《東北師范大學(xué)》2017年碩士論文

【摘要】：本文研究了帶有比率依賴功能反應(yīng)的擴(kuò)散Leslie-Gower系統(tǒng),行波解的存在性.將系統(tǒng)等價(jià)變形為R3中的方程組,并給出最小波速c*.當(dāng)cc*時(shí)行波解不存在;當(dāng)cc*時(shí),用Dunbar所提出的打靶法證明了行波解的存在性.這一方法主要是把Wazewski定理,穩(wěn)定流形定理及LaS alle不變性原理三者結(jié)合起來(lái)使用.首先,應(yīng)用Wazewski定理,構(gòu)造出一個(gè)足夠大的Wazewski集,使得解軌線在+∞處滿足邊界條件,即相空間的解軌線一定位于(u*,v*,0)處的穩(wěn)定流形上.然后,在(1,0,0)的一個(gè)充分小的圓內(nèi)找到一個(gè)Σ集合,并證明存在過(guò)Σ的軌線不會(huì)離開(kāi)W中的一個(gè)有界區(qū)域.利用LaS alle不變性原理證明解軌線趨于正平衡點(diǎn)(u*,v*,0),完成行波解存在性定理的證明.
[Abstract]:In this paper, we study the existence of traveling wave solutions for a diffusive Leslie-Gower system with ratio dependent functional reactions. The system is deformed into the equations in R3, and the minimum wave velocity C ~ (1) is given. The traveling wave solution does not exist at cc* and the existence of traveling wave solution is proved by the shooting method proposed by Dunbar. This method mainly combines Wazewski theorem, stable manifold theorem and LaS alle invariance principle. Firstly, a sufficiently large Wazewski set is constructed by using the Wazewski theorem, so that the solution trajectory satisfies the boundary condition at 鈭，

本文編號(hào)：2031235