This presentation outlines the systematic development of adaptive synchronization frameworks for leader-follower oscillator and pendulum systems, tracing a path from deterministic hybrid regimes to stochastic switching environments. We first establish a fundamental architecture for tracking under deterministic disruptions, including impulsive velocity resets and switched leader frequencies under a common external forcing environment. Using a first-order adaptive law to adjust the follower's natural frequency, we analyze the resulting cascaded error dynamics through composite Lyapunov methods. The analysis shows that unmatched hybrid events introduce structural mismatches that require an input-to-state stability (ISS) framework, while ideal matched resets may remove these mismatch effects and recover exact exponential synchronization. Extending this framework to stochastic switching environments, we focus on the realistic mismatched Markovian regime, where the leader's natural frequency undergoes random abrupt transitions modelled by a continuoustime Markov jump process. Since the follower cannot generally detect or implement these random frequency changes instantaneously, stochastic switching naturally leads to asynchronous operation, with a finite time lag between the leader's transition and the follower's response. During these asynchronous intervals, the frequency mismatch acts as a disturbance input and may temporarily increase the Lyapunov function. Thus, ISS provides the natural stability framework, yielding practical exponential synchronization with an ultimate bound determined by the magnitude, rate, and duration of the asynchronous mismatches. Numerical simulations validate the theoretical results and demonstrate the robustness of the proposed adaptive control strategy in application benchmarks such as robotic pendulums and computer-controlled oscillatory networks.