Periodic Solution for a Two-Species Nonautonomous Competition Lotka–Volterra Patch System with Time Delay1

By 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 0 −τ K 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 .