# The Duffing – Van der Pol Equation : Metamorphoses of Resonance Curves

@inproceedings{Kyzio2015TheD, title={The Duffing – Van der Pol Equation : Metamorphoses of Resonance Curves}, author={Janusz B. Kyzioł and Andrzej Okniński}, year={2015} }

We study dynamics of the Duffing–Van der Pol driven oscillator. Periodic steady-state solutions of the corresponding equation are determined within the Krylov-Bogoliubov-Mitropolsky approach to yield dependence of amplitude on forcing frequency as an implicit function, referred to as resonance curve or amplitude profile. Equations for singular points of resonance curves are solved exactly. We investigate metamorphoses of the computed amplitude profiles induced by changes of control parameters…

## 7 Citations

### Van der Pol-Duffing oscillator: Global view of metamorphoses of the amplitude profiles

- MathematicsInternational Journal of Non-Linear Mechanics
- 2019

### Localizing Bifurcations in Non-Linear Dynamical Systems via Analytical and Numerical Methods

- Mathematics
- 2022

: In this paper, we study the bifurcations of non-linear dynamical systems. We continue to develop the analytical approach, permitting the prediction of the bifurcation of dynamics. Our approach is…

### Exact Solutions and Integrability of the Duffing – Van der Pol Equation

- MathematicsRegular and Chaotic Dynamics
- 2018

The force-free Duffing–Van der Pol oscillator is considered. The truncated expansions for finding the solutions are used to look for exact solutions of this nonlinear ordinary differential equation.…

### Some Novel Approaches for Analyzing the Unforced and Forced Duffing–Van der Pol Oscillators

- Computer ScienceJournal of Mathematics
- 2022

The application of this approach is not limited to (un)forced DVdPV oscillators only but can be applied to analyze many higher-order nonlinearity oscillators for any odd power and it gives more accurate results than other approaches.

### EXACT SOLUTION OF VAN DER POL NONLINEAR OSCILLATORS ON FINITE DOMAIN BY PADE APPROXIMANT AND ADOMIAN DECOMPOSITION METHODS

- Mathematics
- 2021

This paper is concerned with a thorough investigation in achieving exact analytical solution for the Van der Pol (VDP) nonlinear oscillators models via Adomian decomposition method (ADM). The models…

### A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator

- Computer ScienceComput. Phys. Commun.
- 2020

### Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method

- MathematicsMathematics
- 2019

This work deals with a new modified version of the Adomian-Rach decomposition method (MDM). The MDM is based on combining a series solution and decomposition method for solving nonlinear differential…

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