Against the backdrop of frequent fluctuations and risks in financial markets, traditional models struggle to adequately capture the nonlinear interactions and the potential of critical transitions within the market. It is imperative to develop evolutionary models that capture the complex dynamics of financial systems. Based on data from China’s financial markets from 2007 to 2022, this study applies Granger Causality Test to obtain comprehensive market indices with coupling relationships, constructs a nonlinear evolutionary model, and further conducts a stability analysis accordingly. The stability analysis, based on the eigenvalues of the Jacobian matrix, reveals that under the current parameter settings, no locally asymptotically stable equilibrium exists. Therefore, it is necessary to introduce macroeconomic control measures with damping effects to enhance system stability. This research not only offers a new perspective on understanding nonlinear interactions in financial markets, but also provides a quantitative and practical theoretical framework for pro-active risk management and policy formulation.