Dynamic analysis of competing predator-prey systems with pure delays

Abstract

Two classes of nonautonomous three-species Lotka-Volterra type one predator-two competitive prey systems with pure discrete time delays are investigated. Some new sufficient conditions on the boundedness, the permanence, the extinction and the global attractivity of the systems are established by using the comparison method and the construction of suitable Lyapunov functional. Finally, the theoretical results are illustrated by one example with numerical simulations.