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The corticotroph model is a 7th order nonlinear differential equation system derived for representing the action potential dynamics of corticotrophs; one of the endocrine cells that is responsible for stress regulation. Here we use numerical continuation methods to perform bifurcation analysis since controlling bifurcations in the hormonal dynamics may bring some new insights in the treatment of stress related disorders. We study the bifurcation structure of the system as a function of the BK-channel dynamic parameters and the all maximal conductances. We identify the regions of bistability and bifurcations that shape the transitions between resting, bursting and spiking behaviors, and which lead to the appearance of bursting which is directly connected to stress regulation. Furthermore, we find that there are two routes to bursting, one is the experimentally observed BK-channel dynamics and the other is Ca2+ channel conductance only. Finally, we discuss how some of the described bifurcations affect dynamic behavior and can be tested experimentally.