Little is known about the bursting phenomenon, present in underexited adaptive control systems. The bulk of the reported analysis of bursting relies on a time-scale decomposition of the adaptive controller closed loop state-space. Much of the bursting cycle (i.e. drift, burst and recovery) occurs beyond the region of the state-space where the decomposition applies. This paper studies the non-linear interactions between the regressor generation and the adaptive algorithm. It brings insight into the tunning of leakage and dead-zones. We profit from the departure from the traditional approach in gaining qualitative insight into this instability mechanism.