Persistence and Coexistence in a Unidirectional Plant–Pollinator Model with Seasonality
摘要
How does seasonality influence the persistence and coexistence dynamics of plant–pollinator systems? To address this question, we analyze a periodically forced mathematical framework where pollinators exhibit dual ecological roles: as consumers through resource depletion and as mutualists via pollination services. System behavior is classified into four distinct regimes based on net mutualistic effects: predation-dominated, plant-robbing, mutualism-dominated, and mutualism. Employing persistence theory and monotone iteration techniques with upper/lower solutions, we mainly discuss the existence, multiplicity, uniqueness and global attractiveness of coexistence periodic solutions. Numerical bifurcation analysis further reveals bistability between competing periodic attractors. Key results demonstrate fundamental regime-dependent thresholds: in predation-dominated systems, coexistence hinges critically on pollinators’ intrinsic recruitment rates, whereas mutualism-dominated systems require synergistic mutualistic efficiency and sufficient initial population densities—with coexistence failure occurring when pollinator stocks fall below critical baselines. Compared to the autonomous mutualism system dynamics, periodic heterogeneity endows the system with bistability, which in turn benefits the survival of pollinators. The derived results extend to a broad class of non-monotonic time-periodic ecological models.