A seasonal succession model for frog population dynamics with mating behaviors

Mating behaviors significantly influence the dynamics of frog populations. In this study, we formulate a stage-structured model with periodic time delay that reflects the complexities of frog populations, accounting for seasonal changes, two-sex division, mating interactions, and adult competition. The model tracks the fluctuations of female and male populations in both active and hibernation phases. To analyze the global dynamics of this system, we explore fundamental properties in the natural phase space and a new phase space, in the quotient space sense, to establish the strong monotonicity of the solution periodic semiflow. Numerical simulations evaluate the effects of maturity mortality rates and mating pair numbers on population trajectories over single and multiple life cycles. The results indicate that the populations decline markedly prior to hibernation, but an increased number of mating pairs correlates with larger stable population sizes during the active phase.