Hybrid dynamical system model for seasonal mosquito competition with reproductive interference

This paper examines the competition dynamics between two mosquito species, Aedes aegypti and Aedes albopictus, incorporating seasonal effects and reproductive interference based on experimental data. We develop a hybrid model that switches between continuous growth during favorable seasons and discrete overwintering updates, capturing both the asymmetric mating interference observed in laboratory studies and the seasonal constraints in temperate regions. To analyze this complex system, we first characterize the continuous subsystem's global dynamics, then incorporate seasonal switching to derive explicit thresholds determining long-term outcomes. The main contributions include establishing a separatrix that divides initial conditions leading to competitive exclusion, deriving six biologically interpretable thresholds that classify the system's behavior, and proving rigorous stability criteria for single-species states, together with the necessary and sufficient conditions for the existence and uniqueness of the coexistence state. Our approach bridges experimental data and mathematical theory, providing a general framework for analyzing seasonal competition systems. Based on our results, we propose four mathematical questions on basin characterization, convergence time estimation, multistability analysis, and high-dimensional extensions. These questions contribute to advancing both the theory of hybrid dynamical systems and the mathematical modeling of ecological invasions.