<p>In this paper, we study a population dynamics model containing one prey and two predators, combining the Smith growth model, the Holling Type II, and the Monod-Haldane functional response. We introduce time lags, nonlinear suppression terms, and Allee effects. We demonstrate the persistence of the system, showing that under specific parameter conditions, the system is able to maintain the population size within positive values and finite intervals. We also prove the global asymptotic stability of the system near the internal equilibrium point and investigate the effect of the time lag parameter on the stability of the system, which shows that the system will change from steady state to periodic oscillation when the time lag parameter exceeds a certain critical value. In the sensitivity analysis section, we develop the study using two approaches: firstly, the direct method reveals that the system shows high sensitivity to small changes in the time lag parameter in the early stage; and then, by combining the Latin Hypercubic Sampling (LHS) method and the Partial Correlation Coefficients (PRCC), we conduct global uncertainty and sensitivity analyses of the parameters in the system in order to assess the effect of different parameters on the model output. Numerical simulations validate our theoretical derivations and demonstrate the complex behavioral patterns of the system under different time lag conditions. This study provides an important theoretical basis for understanding predator-prey dynamics and suggests a strong methodological support for biodiversity conservation and ecosystem management.</p>