  This paper concerns an age-structured juvenile-adult model with harvesting
pulse and moving boundaries in a heterogeneous environment, in which the moving
boundaries describe the natural expanding front of species and human periodic
pulse intervention is carried on the adults. The principal eigenvalue is
firstly defined and its properties involving the intensity of harvesting and
length of habitat sizes are analysed. Then the criteria to determine whether
the species spread or vanish is discussed, and some relevant sufficient
conditions characterized by pulse are established. Our results reveal that the
co-extinction or coexistence of species is influenced by internal expanding
capacities from species itself and external harvesting pulse from human
intervention, in which the intensity and timing of harvesting play key roles.
The final numerical approximations indicate that the larger the harvesting rate
and the shorter the harvesting period, the worse the survival of all
individuals due to the cooperation among juveniles and adults, and such
harvesting pulse can even alter the situation of species, from persistence to
extinction. In addition, expanding capacities also affect or alter the outcomes
of spreading-vanishing
