 Recent studies on exceptional points, EPS, in non-homission optical systems have shown unique traits such as unidirectional invisibility, chiral mode switching, and laser self-termination. In coupled semiconductor nanolasers, EP singularities can be accessed above the lasing threshold where they become branch points of a non-linear dynamical system. Cavity detuning is necessary for compensating the carrier-induced frequency shift to restore EPS. The pump imbalance at lasing EPS varies with total pump power, enabling continuous tracking. This work uncovers the unstable nature of EPS above laser threshold in coupled semiconductor lasers and offers promising opportunities for self-pulsing nanolaser devices and frequency combs. This article was authored by Kawen Ji, Qi Zhong, Li Ji Yi, and others.