For the problem of vibration in automotive disc brake induced by friction, a minimal two degree of freedom model where the brake pad and brake disc are coupled with variable friction coefficient is presented. Based on Routh-Hurwitz criteria, stability and instability areas of the brake model are analyzed. The range of parameter values and coupled frequencies are identified. By using parameter values which have physical meaning, the relationship between the different angles, the stability and amplitude of limit cycle are illustrated. Based on the bifurcation diagram of two parameters, the rich dynamics phenomena and the existence of chaos in the brake system are explored. The results show that the mass, stiffness of the brake pad and the velocity of brake rotor have a significant effect on the stability of the brake system. The conclusions of this paper are to be significantly referred for the design and control the vibration of the brake system.