Analysis of the Van der Pol Oscillator

The Van der Pol oscillator is a nonlinear system known for its self-sustaining oscillation and behavior. This paper analyzes how the system evolves as the damping parameter μ changes, focusing on equilibrium points, phase plane trajectories, and limit cycles. Throughout the paper, we highlight how the equation also relate to physical systems, such as electrical circuits and biological rhythms, showing the significance and relevance of the Van der Pol oscillator in modeling real-world nonlinear behavior.