We study a 3D conductance-based model of a single thalamocortical (TC) neuron in response to sensorimotor signals. In particular, we focus on the entrainment of the system to periodic signals that alternate between `on´ and `off´ states lasting for time T1 and T2, respectively. By exploiting invariant sets of the system and their associated invariant fiber bundles that foliate the phase space, we reduce the 3D Poincare map to the composition of two 2D maps and also simplify the two components of one of the 2D maps to a uniform shift and a uniform decay. Then based on these 2D maps, we analyze the bifurcations of the entrained limit cycles as the parameters T_1 and T_2 vary.