New aspects of integrability of force-free Duffing–van der Pol oscillator and related nonlinear systems
From MaRDI portal
Publication:4812480
DOI10.1088/0305-4470/37/16/004zbMath1069.34055arXivnlin/0404001OpenAlexW3099240933MaRDI QIDQ4812480
V. K. Chandrasekar, Murugaian Senthilvelan, Muthusamy Lakshmanan
Publication date: 23 August 2004
Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/nlin/0404001
Explicit solutions, first integrals of ordinary differential equations (34A05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)
Related Items
Let's Lie: A miraculous haul of fishes ⋮ A Systematic Method of Finding Linearizing Transformations for Nonlinear Ordinary Differential Equations I: Scalar Case ⋮ Complex dynamical properties of coupled Van der Pol–Duffing oscillators with balanced loss and gain ⋮ A generalization of the \(S\)-function method applied to a Duffing-van der Pol forced oscillator ⋮ On the complete integrability and linearization of nonlinear ordinary differential equations. II. Third-order equations ⋮ First integrals and exact solutions of a class of nonlinear systems ⋮ Completely integrable dynamical systems of Hopf-Langford type ⋮ Invariant surfaces and Darboux integrability for non-autonomous dynamical systems in the plane ⋮ Hypergeometric first integrals of the Duffing and van der Pol oscillators ⋮ Exact solutions and integrability of the Duffing-van der Pol equation ⋮ Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems ⋮ Analytic approximate solutions of the cubic-quintic Duffing-van der Pol equation with two-external periodic forcing terms: stability analysis ⋮ A nonconvex dissipative system and its applications. I ⋮ Application of extended Prelle--Singer procedure to the generalized modified Emden type equation ⋮ On the integrability of Liénard i-type equations via \(\lambda \)-symmetries and solvable structures ⋮ On the complete integrability and linearization of certain second-order nonlinear ordinary differential equations ⋮ Analytical solution of the damped Helmholtz-Duffing equation ⋮ First integrals for the damped Helmholtz oscillator ⋮ An investigation of solving third-order nonlinear ordinary differential equation in complex domain by generalising Prelle-Singer method ⋮ \({\lambda}\)-symmetries of some chains of ordinary differential equations ⋮ Solutions of the force-free Duffing-van der Pol oscillator equation ⋮ Nonlocal symmetries of Riccati and Abel chains and their similarity reductions ⋮ A simple and unified approach to identify integrable nonlinear oscillators and systems