Study of Dynamic Systems Based on Lyapunov Stability Theory

Lyapunov Stability Theory provides a robust mathematical framework for analyzing the stability of dynamic systems, widely applied in computational models, automated control systems, and other engineering domains. This paper explores the application of Lyapunov Stability Theory by examining its role in modeling system dynamics under varying parameter conditions. First, a set of differential equations was constructed to describe system behavior across different time intervals. Next, the local stability of equilibrium points was evaluated using Lyapunov Stability Theory. Predictive simulations were then performed by inputting relevant parameters to analyze system stability under changing conditions. Finally, the effects of parameter shifts on system interactions were independently assessed. The results indicate that parameter variations significantly influence system dynamics, potentially amplifying imbalances and intensifying disruptions within interconnected subsystems.