Dynamic Analysis of a Periodic Impulsive Switching Model for a Stage-Structured Single Population With Hibernation Habits

In this paper, we develop a periodic impulsive switching stage-structured model to investigate the population dynamics of species exhibiting hibernation behavior. The model incorporates stage structure (larvae and adults), birth pulses occurring exclusively in the active season, and impulsive harvesting events taking place immediately after hibernation. By combining switched dynamical systems with impulsive differential equations, we accurately capture the seasonal alternation between active and dormant states along with discrete reproductive and harvesting pulses. Using the Jury criterion, we establish sufficient conditions for the local asymptotic stability of both the population extinction periodic solution and the positive periodic solution. Furthermore, we identify an explicit extinction-survival threshold Γ and analyze how key parameters such as hibernation duration, harvesting rate, and birth pulse intensity govern population persistence. Numerical simulations not only validate the analytical results but also uncover complex nonlinear dynamics, including period-doubling bifurcations and chaotic oscillations, as the birth coefficient increases. These findings provide theoretical insights for wildlife conservation and sustainable harvesting strategies concerning hibernating species.