Positive almost periodic solutions for a predator-prey Lotka-Volterra system with delays

摘要

In this paper, by using Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost periodic solutions are obtained for the predator-prey Lotka-Volterra competition system with delays egin{eqnarray*} left{egin{array}{lll} rac{{mathrm{d}} u_i(t)}{{mathrm{d}}t}&=&u_i(t)igg [a_i(t)-sumlimits_{ l=1}^{n}a_{il}(t)u_l(t-sigma_{il}(t))-sumlimits_{j=1}^{m}b_{ij}(t)v_j(t-au_{ij}(t))igg],i=1,ldots,n, rac{{mathrm{d}} v_j(t)}{{mathrm{d}} t}&=&v_j(t)igg[-r_j(t)+sumlimits_{l=1}^{n}d_{jl}(t)u_l(t-delta_{jl}(t))-sumlimits_{h=1}^{m}e_{jh}(t)v_h(t-heta_{jh}(t))igg ], j=1,ldots,m, end{array}ight. end{eqnarray*} where $a_i,r_j, a_{il}, b_{ij},d_{jl},e_{jh}in C(mathbb{R},(0,infty)sigma_{il},au_{ij},delta_{jl},heta_{jh}in C(mathbb{R},mathbb{R})(i,l=1,ldots,n, j,h=1,ldots,m)$ are almost periodic functions.