To overcome the high computational costs and overly smooth node embeddings in traditional graph convolutional networks for complex dynamic data processing, researchers proposed a graph convolutional network based on reservoir dynamics (RGC-Net). This model combines reservoir dynamics principles with structured graph convolution, enhancing feature retention by fixing random reservoir weights and using leakage integrators. The study constructed a robust adaptive model suitable for graph classification and a graph generation transformer for dynamic brain connection analysis. Experimental results show that RGC-Net achieves advanced performance in both classification and generation tasks, achieving faster convergence and effectively mitigating over-smoothness. The relevant source code has been made open source.