| Abstract: | 本計畫中，我們探討以下捕食者－被捕食者系統之行進波解u_t=d_1 u_xx+ru(1-u)-rkuv,v_t=d_2 v_xx+sv(1-v/u), 其中u(x,t)和v(x,t)分別代表捕食者和被捕食者在時刻t位置x的數量密度，d_1,d_2,r,s皆為正參數，d_1, d_2為兩種族群的擴散係數，r,s為族群成長速率，rku為捕食者的功能反應，ru(1-u)為被捕食者的logistic成長速率，其承載力(carrying capacity)已正規化為1，而捕食者的承載力和被捕食者的數量密度成比例。
In this project, we study traveling wave solutions of the following diffusive predator-prey systemu_t=d_1 u_xx+ru(1-u)-rkuv,v_t=d_2 v_xx+sv(1-v/u), where u(x,t) and v(x,t) denote the population densities of prey and predator species at time t and location x, respectively, d_1,d_2,r,s are positive parameters such that d_1, d_2 are diffusion coeffcients and r,s are intrinsic growth rates of species u,v, respectively, rku is the functional response to the predator population, ru(1-u) is the logistic growth rate of the prey and its carrying capacity is normalized to be 1. The density of predator follows a logistic dynamics with a varying carrying capacity proportional to the density of prey. |
