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  • On an age-structured juveni...
    Xu, Haiyan; Lin, Zhigui; Zhu, Huaiping

    Journal of Differential Equations, 10/2024, Volume: 405
    Journal Article

    This paper concerns an age-structured juvenile-adult model incorporating harvesting pulse and moving boundaries in a heterogeneous environment, in which harvesting reflects human periodic pulse intervention on adults and the moving boundaries describe the natural expanding front of species. The principal eigenvalue is firstly defined and its properties involving the intensity of harvesting and length of habitat sizes are analyzed. 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 capacity from species itself and external harvesting pulse from human intervention, in which the intensity and timing of harvesting play key roles. Our numerical simulations validate that the larger the harvesting rate and the shorter the harvesting period, the worse the survival of the species 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 and vanishing.