Examining the Van der Pol Oscillator: Stability and Bifurcation Analysis
F. A. Chughtai (National University of Sciences, Technology,, Islamabad, Pakistan)
TL;DR
This paper analyzes the stability and bifurcation behavior of the Van der Pol oscillator, comparing analytical and numerical solutions, and exploring how different parameters influence its dynamics.
Contribution
It provides a detailed bifurcation analysis of the Van der Pol oscillator using both analytical methods and numerical simulations, highlighting new insights into its nonlinear behavior.
Findings
Analytical solutions align well with numerical results.
Bifurcation scenarios vary with control parameters.
Limit cycle behavior is characterized at different nonlinear damping levels.
Abstract
In this paper, Van der pol equation has been analyzed for stability and bifurcation phenomena with and without forcing component. Analytical solution of the Van der pol equation using Method of Multiple Scales (MMS) is compared with numerical results obtained using MATLAB ode45 solver. Limit cycle analysis has been performed at increasing order of nonlinear damping term. Different scenarios of bifurcation have been studied with variation in control parameters.
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Taxonomy
TopicsVibration and Dynamic Analysis · Probabilistic and Robust Engineering Design · Fractional Differential Equations Solutions