Positive Periodic Solutions For A Neutral Lotka-volterra System With State Dependent Delays

摘要

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 (dx_i(t))/(dt) = x_i(t) [r_i(t) ∑~n_(j÷1) a_(ij)X_j(t)＋∑~n_(j=1) b_(ij)(t)X_j(t-τ_(ij)(t, x_1(t), ..., x_n(t))) ＋∑~n_(j-1) 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.