Addressing the core limitations inherent in STGCN (spatial-temporal graph convolutional network) for traffic flow prediction. First, it remains challenging to concurrently capture the periodic patterns (e.g., daily/weekly peaks) and abrupt variation characteristics (short-term traffic fluctuations) of traffic flow. Second, the static graph structure is incompetent in accommodating the time delay effects across distinct regions and time intervals, culminating in inadequate characterization of dynamic spatio-temporal dependencies. A traffic flow prediction model, WR-MDGCRN (wavelet-based residual multi-branch dynamic graph convolutional recurrent network), was proposed. Specifically, the model decouples the low-frequency (periodic) and abrupt variation components of traffic flow via wavelet decomposition, captures local abrupt variations and node propagation through graph wavelet convolution integrated with GRU (gated recurrent unit), and investigates global dynamic spatio-temporal dependencies by leveraging dynamic graph convolution combined with dynamic graph generation. Additionally, residual connections are incorporated to reinforce information transmission and mitigate gradient vanishing, with prediction results yielded through a fusion layer. Experiments implemented on the PEMSD4 and PEMSD8 datasets demonstrate that, in comparison with existing state-of-the-art algorithms, the WR-MDGCRN achieves an average improvement of 4.96%, 3.41%, and 11.14% in MAE (mean absolute error), RMSE (root mean squared error), and MAPE (mean absolute percentage error), respectively. Furthermore, the model exhibits superior stability under diverse time steps and traffic scenarios, which fully validates its efficacy and generalization capability.