Existence and global attractivity of positive periodic solutions for delay Lotka–Volterra competition patch systems with stocking ✩

By means ofMawhin’s continuation theorem of coincidence degree and Lyapunov functional, a set of easily verifiable criteria are established for the existence and global attractivity of positive periodic solutions for delay Lotka–Volterra competition patch system with stocking x 1 (t ) = h1 t,x1(t ) a1(t )− b1(t)x1(t )− c1(t)y(t ) +D1(t ) x2(t −τ1)− x1(t ) + S1(t ), x 2 (t ) = h2 t,x2(t ) a2(t )− b2(t)x2(t ) +D2(t ) x1(t − τ2)− x2(t ) + S2(t ), y (t ) = h3 t,y(t) a3(t )−b3(t)y(t )− β(t) 0 −τ k(s)y(t + s)ds − c3(t)x1(t ) + S3(t ). Some known results are generalized and improved.  2004 Elsevier Inc. All rights reserved