Periodic Solution for a Two-Species Nonautonomous Competition Lotka–Volterra Patch System with Time Delay

AbstractBy using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a two-species nonautonomous competition Lotka–Volterra patch system with time delay,x′1(t)=x1(t)[r1(t)−a1(t)x1(t)−b1(t)y(t)]+D1(t)[x2(t)−x1(t)],x′2(t)=x2(t)[r2(t)−a2(t)x2(t)]+D2(t)[x1(t)−x2(t)],y′(t)=y(t)r3(t)−a3(t)x1(t)−b3(t)y(t)−β(t)∫−τ0K(s)y(t+s)ds,is established, where ri(t),ai(t)(i=1,2,3),Di(t)(i=1,2),bi(t)(i=1,3), and β(t) are all positive periodic continuous functions with period w>0,τ is a nonnegative constant, and K(s) is a continuous nonnegative function on [−τ,0]