DYNAMICS OF A PERIODIC STAGE-STRUCTURE COMPETITIVE MODEL WITH TWO MATURATION DELAYS

Considering that many populations are affected by seasonal fluctuations in tem-perature in the process of growth, and there is a general competitive relationship between populations, in this paper, a stage-structured two species competitive model with two periodic maturation delays is proposed to study the effect of temperature and maturation delays on population dynamics. Firstly, we give the formulation of the model combining with biological significance. Then, criteria on the global dynamics of the whole model are obtained based on the basic reproduction ratio R0: when R0 < 1, the all populations is extinction, and when R0 > 1, the all populations is persistent, i.e., all solutions of system stabilize at a positive periodic state. Furthermore, we discuss the effect of temperature and length of maturation delays on the population density by numerical simulations, which implies larger temperature variation can decrease the minimum population densities and the maturation time may change the stability of the system.