Positive periodic solutions for a neutral Lotka–Volterra system with state dependent delays

By using a fixed point theorem of strict-set-contraction, some new criteria are established for the existence of positive periodic solutions of the following periodic neutral Lotka–Volterra system with state dependent delays d x i ( t ) d t = x i ( t ) r i ( t ) - ∑ j = 1 n a ij ( t ) x j ( t ) + ∑ j = 1 n b ij ( t ) x j ( t - τ ij ( t , x 1 ( t ) , … , x n ( t ) ) ) + ∑ j = 1 n c ij ( t ) x j ′ ( t - σ ij ( t , x 1 ( t ) , … , x n ( t ) ) ) , i = 1 , 2 , … , n , where r i , a ij ∈ C ( R , R + ) , b ij , c ij ∈ C ( R , R ) ( i , j = 1 , 2 , … , n ) are ω-periodic functions and τ ij , σ ij ∈ C ( R n + 1 , R ) ( i , j = 1 , 2 , … , n ) are ω-periodic functions with respect to their first arguments, respectively.