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A piecewise smooth system is characterized by non-differentiability on a curve in the phase space. In this paper, we discuss particular bifurcation phenomena in the dynamics of a piecewise smooth system. We consider a two-dimensional piecewise smooth system which is composed of a linear map and a nonlinear map, and analyze the stability of the system to determine the existence of dangerous border-collision bifurcation. We finally present some numerical examples of the bifurcation phenomena in the system.