The theorems for testing the local activity in one-port cellular neural/nonlinear network (CNN) cells with four local state variables are presented. Using the theorems computes the bifurcation diagrams of the cardiac Purkinje fiber (CPF) equations which describe the long-lasting action and pace-maker potentials of the Purkinje fiber of the heart. The computer simulation shows that periodic trajectories or convergent trajectories of the CPF Equations can be found if the corresponding cell parameters are located in a positive domain but nearby edge of chaos. In particular, a heart with approximate normal frequency of heartbeat but non-normal electrocardiogram may suddenly stop beating by slightly perturbing the parameters of the corresponding CPF Equations when the parameters are located nearby the edge of chaos in the bifurcation diagrams. This research seems to interpret reasonably the phenomena that patients with cardiac diseases might suddenly die without warning.