摘要
一、引言文献对“Ⅱ类功能反应模型”进行了详细、完整的分析,给出了存在周期解的充分条件.但是在自然界中,就某一生态环境而言,往往同时存在上千种,甚至上万种“食饵-捕食者”系统,在食饵和捕食者之间都存在竞争关系.考虑到这些因素,本文将考虑更一般的高维“食饵-捕食者”模型.
In this paper we consider the system in which there are n “prey-preda- tor” s in the same ecological environment with competition: (dx_i(t))/(dt)=x_i(a_i-b_ix_i)-(α_ix_iy_i)/(1+w_ix_i)+εx_if_i(x_1,…x_(i-1),x_(i+1)…,x_n), (dy_i(t))/(dt)=y_i(-d_i+(e_iαx_i)/(1+w_ix_i)+εy_ig_i(y_i,…,y_(i-1),y_(i+1),…,y_n), i=1,…,n,0≤x_i≤∞,0≤y_i≤∞. Here x_i(t) is the total number or the density of the ith prey,y_i (t) is the total number or density of the ith predator.The other parameters all bear eco- logical meaning. For high dimensional ordinary differential equations,the existence of periodic soluton is a rather complicated problem.In this paper,an existence theorem of a periodic solution for the general system. (dx_i)/(dt)=f_i(x_i)+εF_i(t,x_i,…,x_n),i=1,2,…,n, x_i(t),f_i,F_iεR^n is proved and from which follows the existence of perio- dic solution for our model.
出处
《生物数学学报》
CSCD
北大核心
1989年第2期165-174,共10页
Journal of Biomathematics
