This paper contributes a computational analysis of the interplay of different forms of adaptivity (connectivity learning and synchrony-induced adaptivity) involved in empathic responding, synchronization and bonding between an AI Coach and its user under stressful circumstances. The analysis is performed using an adaptive network modeling approach based on self-modeling networks. It integrates concepts from neuroscience such as plasticity by connectivity learning and metaplasticity to control plasticity and concepts from social psychology such as social contagion, synchronization and related bonding. It is shown how such a human-like AI Coach can strengthen its empathic responses and bonding in which connectivity learning and synchrony-induced adaptivity each contribute uniquely to this adaptation process. It was found that decreasing one of two types of adaptation has not the same effect during the process as decreasing the other type. Both types of adaptation ultimately result in a strong capability of the AI Coach to bond, although somewhat stronger effects were found for connectivity learning. Future work can further design this AI coach by equipping it with an user interface and evaluating its performance in real-world stressful contexts such as in cybersecurity teams.