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

AbstractBy means of Mawhin'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)∫−τ0k(s)y(t+s)ds−c3(t)x1(t)]+S3(t). Some known results are generalized and improved