EXISTENCE OF POSITIVE SOLUTION FOR A TWO—PATCHES COMPETITION SYSTEM WITH DIFFUSION AND TIME DELAY AND FUNCTIONAL RESPONSE

摘要

By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two-patches competition system with diffusion and time delay and functional response ｛x′(t)=x1(t)[a1(t)-b1(t)x1(t)-c1(t)y(t)/[1+m(t)x1(t)]]+D1(t)[x2(t)-x1(t)],;x′2(t)=x2(t)[a2(t)-b2(t)x2(t)-c2(t)∫-r0 k(s)x2(+s)ds]+D2(t)[x1(t)-x2(t)],；y′(t)=y(t)[a3(t)-b3(t)y(t)-c3(t)x1(t)[1+m(t)x1(t)]] is established,where ai(t),bi(t),ci(t)(i=1,2,3),m(t)and Di(t)(i=1,2)are all positive periodic continuous functions with period w>0,r is a nonnegative constant and k(s)is a continuous nonnegative function on [-r,0]。