The Bonhoffer-van der Pol (BVP) oscillator is a two-dimensional autonomous system, which can exhibit many nonlinear phenomena for various inputs [3,4]. The extended BVP oscillator forms a simple circuit by addition of a capacitor to the BVP oscillator, further exhibiting a three-dimensional autonomous system. Oscillations, non-scintillation, and many nonlinear phenomena were observed in case of the extended BVP oscillator . Even torus was observed by using the specific nonlinear resistor . In this chapter, we investigate in detail, the bifurcation phenomena in the extended BVP oscillator. First, we reveal bifurcations of the parameter region of chaos attractors with two-parameter bifurcation diagrams computed by adopting the shooting method [6,7], based on numerical integration of variational equations. Second, we discussed an application with relation to the oscillator-chaos synchronization. When we coupled these two oscillators by a resistor, inphase and antiphase chaos synchronization was obtained. We illustrated a bifurcation diagram for these coupled oscillator.