<p>This paper presents a comprehensive mathematical model of an arched-beam structure in a simulated MEMS resonator to analyze its complex nonlinear dynamics. The model captures the intricate interactions and nonlinearities inherent in the system, serving as a foundation for understanding its dynamic behavior. A combination of analytical and numerical methods is employed to investigate the chaotic phenomena present in the resonator thoroughly. Potential energy functions are derived to characterize the system’s stability landscape, phase portraits are constructed to visualize its dynamic trajectories, and bifurcation diagrams are generated to explore the transitions between different dynamic regimes under varying system parameters. These analyses reveal the presence of chaotic behavior and provide crucial insights into the underlying mechanisms driving such dynamics. Building upon this analysis, this paper introduces an intelligent agent designed to control chaos in the system. This agent utilizes the Deep Q-Network algorithm, integrating deep learning with reinforcement learning to acquire optimal control strategies in high-dimensional and nonlinear environments. To demonstrate the feasibility and efficiency of the proposed control strategy, experimental studies are conducted. The results demonstrate that the intelligent control agent not only successfully suppresses chaotic behavior but also achieves performance metrics that closely align with those predicted by numerical simulations.</p>