Modelling And Simulation Of Non-Linear Analysis Of The Cardiovascular System

Abstract

The physiological oscillators produce oscillations, in the form of stable, closed trajectory called a limit cycle. These oscillations exhibit the phenomenon of frequency entrainment or phase locking. These are analyzed by presenting Vanderpol oscillator. Vanderpol oscillator is a non-linear oscillator. In the non-limit cycle oscillator, external disturbance move the phase trajectory to different orbit around the centre and will not come to original  point, where as in limit cycle oscillator, the phase trajectory returns to its original location. When Vander Pol oscillator is driven by the external frequency, which is different with natural frequency of the oscillator, then the resultant output is mixture of components that result from the interaction of the driving periodicity on natural oscillations. If the external frequency is equal to natural frequency of vendorpol oscillator, then nonlinear system will adopt the external frequency. The time courses of oscillatory activity of heart and phase trajectories are generated by Vanderpol model and simulated using the Simulink. The response of VanderPol oscillator for various external frequencies is also obtained.