<p>Aeroengine performance is directly influenced by the state of the gas path system. Under multi-source random excitation, it displays complicated nonlinear stochastic dynamics features that lead to ambiguous transmission laws of random excitation effects and unclear stochastic response characteristics of gas path parameters, potentially endangering engine performance. The features of a gas path system under random excitations of inlet and combustion heat are investigated for the first time in this work on stochastic dynamics. A synchronous solution technique is proposed for analyzing the stochastic response properties of high-dimensional gas path parameters, and a corresponding nonlinear stochastic dynamics model is developed. The evolution law of the stochastic response characteristics, the transmission characteristics of the stochastic excitation effects, and the interaction characteristics of the multi-source random excitation are revealed by studying the stochastic response characteristics and distribution features of gas path parameters. The findings show that the stochastic response of gas path systems displays single-peak, double-peak, and multi-peak features, and peak switching happens under coupled random excitations. Continuous peak fluctuations are a hallmark of the evolutionary process, and the stochastic response variance first increases gradually before suddenly increasing. The influence of random excitation spreads fast via mechanical rotation, whereas it spreads more slowly via the changes in the internal working fluid state of the component. Compared to the temperature parameters, the component pressure parameters show a more sensitive response. Finally, the analysis results are validated using data from the flight test. The knowledge foundation this work offers is crucial for optimizing overall performance, evaluating component performance, and ensuring reliable and stable operation of gas path systems under multi-source random excitation.</p>