Theorems for Testing Local Activity of CNN and Application to cardiac Purkinje Equations

The theorems for testing the local 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 (CPE) 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 foun if the cormsponing 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 by slightly perturbing the parameters of the corresponding CPF Equations when the Paramders 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.