ABSTRACT
The Bonhoffer-van der Pol (BVP) oscillator is a two-dimensional autonomous system, which can exhibit many nonlinear phenomena for various inputs. This chapter investigates the bifurcation phenomena in the extended BVP oscillator. It explains bifurcations of the parameter region of chaos attractors with two-parameter bifurcation diagrams computed by adopting the shooting method, based on numerical integration of variational equations. Chaos synchronization is considered to be the most successful application of secure communication methods. Bifurcation phenomena of coupled and simple chaos generator circuits assisted in the study of chaos synchronization. The chapter investigates the existence of complete chaos synchronization in diffusively coupled two extended BVP oscillators. The single BVP oscillator did not have a chaos attractor, but complete antiphase and inphase synchronization and its bifurcations, chaos, and torus in the weakly coupling strength could be observed in the coupled BVP oscillators.
