Modified van der pol (Vdp) oscillator based cardiac pacemakers

Abstract

The paper involves the study of nonlinear dynamics oscillator and numerical methodology to analyze and resolute the nonlinear dynamics model. Based on either the classical Vander Pol oscillator or other nonlinear oscillators, these models were interesting rather because of the physical phenomena that could be obtained (chaos and synchronization). Here, we can simulate many important physiological features of true physiological action potentials in practical systems by adjusting the parameter. We also show different ways to change pacemaker actions. As van der pol oscillator can model heart beat phenomenon so here these oscillator models are modified so that they can match well with the results obtained by actual pacemakers. We model electrical activity of cardiac electric system including a trial and ventricular muscles solving a set of coupled nonlinear oscillator equations. A new mathematical model for the electrical activity of the heart is proposed. In this paper a modified Vander Pol oscillator model was designed in order to reproduce the time series of the action potential generated by a natural pacemaker of the heart (i.e., the SA or the AV node). The model represents a special singularly perturbed three-dimensional system of ordinary differential equations with one fast and two slow variables.