Positive periodic solutions of periodic 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 delaysdxi(t)dt=xi(t)[ri(t)−∑j=1naij(t)xj(t)−∑j=1nbij(t)xj(t−τij(t,x1(t),…,xn(t)))−∑j=1ncij(t)xj′(t−σij(t,x1(t),…,xn(t)))],i=1,2,…,n, where ri,aij,bij,cij∈C(R,R+)ri,aij,bij,cij∈C(R,R+) (i,j=1,2,…,ni,j=1,2,…,n) are ω  -periodic functions and τij,σij∈C(Rn+1,R)τij,σij∈C(Rn+1,R) (i=1,2,…,ni=1,2,…,n) are ω-periodic functions with respect to their first arguments, respectively.