On the Solution of the Van der Pol Equation
Mayer Humi
TL;DR
This paper introduces a method to linearize and solve the Van der Pol equation, including variants with additional nonlinear terms, using a generalized Cole-Hopf transformation, and classifies related Lienard equations.
Contribution
It presents a novel generalized Cole-Hopf transformation for linearizing the Van der Pol equation and classifies certain Lienard equations that can be linearized by this method.
Findings
Successful linearization of the Van der Pol equation with added nonlinear terms.
Classification of low-order polynomial Lienard equations linearizable by the transformation.
Potential for broader application to nonlinear differential equations.
Abstract
We linearize and solve the Van der Pol equation (with additional nonlinear terms) by the application of a generalized form of Cole-Hopf transformation. We classify also Lienard equations with low order polynomial coefficients which can be linearized by this transformation.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Advanced Differential Equations and Dynamical Systems · Chaos control and synchronization