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Under parametric variations, the phase portraits of a dynamical system such as a power system undergoes qualitative changes at bifurcation points. Several global codimension-two bifurcation points such as Zero-Hopf, generalized Hopf, Bogdanov-Takens, among others, can move the system much close to its instability limit, and lead to chaos. Due to this fact, there has been major effort in understanding these instability phenomena, in order to design control and preventive actions for power systems. In this paper, the dynamics of a straightforward system which includes a single machine-infinite bus power system (SMIB) is analyzed. The system is forced to operate under several conditions in order to study its behavior close to codimension-two bifurcation points. This paper is specifically oriented to analyze the Zero-Hopf and the Bogdanov Takens bifurcations, which contributes significantly to the system dynamics.