Van der Pol model in two-delay differential equation representation

Abstract

The Van der Pol equation is the mathematical model of a second-order ordinary differential equation with cubic nonlinearity. Several studies have been adding time delay to the Van der Pol model. In this paper, the differential equation of the Van der Pol model and the RLC (resistor–inductor–capacitor) circuit are deduced as a delay differential equation. The Van der Pol delay model contains two delays, which allows the re-use of its applications in the suggested equation. The Taylor series was used to deduce ordinary differential equations from the delay differential equations in the case of small delays. Also, the model for Parkinson's disease modification is described as the Van der Pol model. A numerical simulation of the delay differential equations has been done to show the different cases that the delay differential equations can express using the MATLAB program.