Hopf Bifurcation Analysis of the BVAM Model for Electrocardiogram

Bio-electric activity of the heart is modeled by the Barrio–Varea–Aragon–Maini (BVAM) model that covers normal rhythm and several arrhythmia that lie in the chaotic region and exhibits several bifurcations. In this chapter, we develop the analytic solution of the BVAM model and identify the Hopf bifurcation. The center manifold reduction is applied to the governing equations to reduce the order of the system. The method of multiple scales is employed to develop the normal form of the Hopf bifurcation for the center manifolds. These are then transformed back into original coordinates where the analytical solution is compared with the numerical solution.