【摘要】：在傳染病動(dòng)力學(xué)中,行波解表示一種傳染源以常數(shù)波速在空間的傳播.本文研究一類(lèi)解耦的SI系統(tǒng) 行波解的存在性.主要研究方法是改進(jìn)的打靶法,利用打靶法,構(gòu)造一個(gè)Σ集,在Σ集內(nèi)找到全局正解,證明當(dāng)t→-∞時(shí),它收斂到無(wú)病平衡點(diǎn);利用Liapunov函數(shù),證明系統(tǒng)全局正解當(dāng)t→∞時(shí),收斂到地方病平衡點(diǎn),即行波解是存在的,再利用數(shù)值模擬去驗(yàn)證所得到的結(jié)果.改進(jìn)的打靶法的優(yōu)勢(shì)在于不需要構(gòu)造復(fù)雜的Wazewski′s集,且能計(jì)算最小波速.
[Abstract]:In infectious disease dynamics, traveling wave solutions represent the spatial propagation of an infectious source at a constant wave velocity. In this paper, we study the existence of traveling wave solutions for a class of decoupled SI systems. The main research method is the improved shooting method. By using the shooting method, a 危 set is constructed and the global positive solution is found in the 危 set. It is proved that when t-鈭，

本文編號(hào)：2434378