On a Juvenile-Adult Model: The Effects of Seasonal Succession and Harvesting Pulse

Abstract

In this paper, a juvenile-adult population model incorporating seasonal succession and pulsed harvesting is developed. The seasonal succession captures the cyclical change between favorable and unfavorable environmental conditions, while the pulsed harvesting represents a periodic human intervention, targeting the adult population exclusively during favorable seasons. The principal eigenvalue for the corresponding linearized system is defined and its dependence on both the intensity of the harvesting pulses and the duration of the unfavorable season is analyzed. Explicit expressions and analysis of the principal eigenvalue for a logistic model extended with seasonal succession and pulsed harvesting are provided specifically. Based on the principal eigenvalue, we establish sufficient conditions for population persistence and extinction. Numerical simulations are conducted to validate these analytical results. Our findings demonstrate that higher harvesting intensity during the favorable season is detrimental to species survival. Furthermore, extending the duration of the unfavorable season can trigger a critical transition from population persistence to extinction.