Dynamic Modeling and Stability Analysis of Complex System Based on PGNN

Aiming at the problem of modeling the dynamics of complex systems driven by heterogeneous data from multiple sources, this paper proposes a graph neural network architecture (PGNN) that incorporates physical constraints. The model characterizes the internal interactions of the system by constructing a heterogeneous graph structure, introduces a spatio-temporal convolution module to capture the dynamic evolution features, and embeds control equation constraints to ensure the physical consistency of the model predictions. Experiments show that the PGNN exhibits significant advantages in system stability analysis, with a 32<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%</sup> improvement in prediction accuracy and a 45% improvement in feature extraction efficiency compared to traditional methods. The nonlinear effect of system parameter thresholds on stability is verified by Jacobi matrix eigenvalue analysis. This study provides a new methodological framework for modeling complex dynamics in industrial process control, intelligent robotic systems, etc. It shows strong robustness in parameter sensitivity tests, and the maximum relative error is controlled within 5%.