Positive periodic solutions for a neutral delay Lotka–Volterra system

Abstract

Applying a fixed point theorem of strict-set-contraction, some new criteria are established for the existence of positive periodic solutions for a class of neutral delay Lotka–Volterra systems: x i ′ ( t ) = x i ( t ) [ r i ( t ) − ∑ j = 1 n a i j ( t ) x j ( t ) − ∑ j = 1 n b i j ( t ) x j ( t − τ i j ( t ) ) − ∑ j = 1 n c i j ( t ) x j ′ ( t − σ i j ( t ) ) ] , i = 1 , 2 , … , n . Compared to known results, our main generalization is that delays of the derivatives are not assumed to be constants, and our results are more easily verifiable.