<p>Coupled with the dynamic evolution characteristics influenced by policy interventions, external environmental factors, and user behaviors, the complex nonlinear interactions among supply, demand, and matching rate in urban taxi carpooling systems, pose significant challenges to the stability regulation of carpooling systems. However, a general modeling framework that balances system stability and regulatory complexity is still lacking. To address this gap, this study constructs a three-dimensional nonlinear dynamical system model integrating carpooling supply, demand, and matching rate. Utilizing the Chengdu dataset from the Didi Smart Mobility Platform and conducting local stability analysis and numerical simulations, this study systematically evaluates the effects of different regulatory strategies on system stability. The results reveal significant parameter threshold effects: the relative change coefficient of carpooling supply has a clear stable range, beyond which the system transitions into periodic oscillations or instability; the demand satisfaction coefficient also exhibits an optimal stable interval, beyond which system stability deteriorates markedly. Strategy comparison demonstrates that, compared with single-parameter strategies and combined strategies, the proposed cross-regulation strategy achieves faster system convergence to equilibrium and exhibits superior performance in stabilizing the supply–demand system. The model accurately captures nonlinear dynamic characteristics, providing a theoretical framework for policy simulation and practical guidance for collaborative platform-government governance.</p>