Positive periodic solutions of nonautonomous delay competitive systems with weak Allee effect

This paper considers a nonautonomous Lotka–Volterra type multispecies competitive system with weak Allee effect and delays. The model has the intraspecific competition terms defined by sign changing functions which depend on population density monotonically and time periodically. An existence theorem of positive periodic solutions is established using the coincidence degree theory. Furthermore, for the case of constant delays, a sufficient condition for the positive periodic solution to be globally attractive is proved with the Lyapunov method so that the system attains permanence.