Existence of positive periodic solutions for neutral delay Gause-type predator–prey system

Abstract

By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions for neutral delay Gause-type predator–prey system. x ′ ( t ) = x ( t ) [ r ( t ) - a ( t ) x ( t - σ ( t ) ) - b ( t ) x ′ ( t - σ ( t ) ) ] - ϕ ( t , x ( t ) ) y ( t - τ 1 ( t ) ) , y ′ ( t ) = y ( t ) [ - d ( t ) + h ( t , x ( t - τ 2 ( t ) ) ) ] . In addition, our results are applicable to neutral delay predator–prey systems with different types of functional responses such as Holling-type II and Ivlev-type.