On a periodic predator–prey system with time delays on time scales

With the help of a continuation theorem based on Gaines and Mawhin’s coincidence degree theory, easily verifiable criteria are established for the global existence of positive periodic solutions of the predator–prey system with time delays on time scales x 1 Δ ( t ) = a 1 ( t ) - b 1 ( t ) exp { x 1 ( t - τ 1 ( t ) ) } - c ( t ) exp { x 2 ( t - τ 2 ( t ) ) } 1 + m exp { x 1 ( t ) } , x 2 Δ ( t ) = - a 2 ( t ) + b 2 ( t ) exp { x 1 ( t - τ 2 ( t ) ) } 1 + m exp { x 1 ( t - τ 2 ( t ) ) } , where a i , b i , c , τ i ∈ C ( T , R + ) , i = 1 , 2 are T-periodic functions.