A Class of Isochronous and Non-Isochronous Nonlinear Oscillators

Abstract

In this work, we present a method of generating a class of nonlinear ordinary differential equations (ODEs), representing the dynamics of appropriate nonlinear oscillators, that have the characteristics of either amplitude independent frequency of oscillations or amplitude dependent frequency of oscillations from the integrals of the simple harmonic oscillator equation. To achieve this, we consider the case where the integrals are in the same form both for the linear and the nonlinear oscillators in either of the cases. We also discuss the method of deriving the associated integrals and the general solution in harmonic form for both the types. We demonstrate the applicability of this method up to 2N coupled first order nonlinear ODEs in both the cases. Further, we illustrate the theory with an example in each case.

arXiv comment19 pages, 3 figures, Accepted for publication in Eur. Phys. J. Spec. Top

References in corpus (13)

• A non-linear Oscillator with quasi-Harmonic behaviour: two- and $n$-dimensional Oscillators
• A remark on rational isochronous potentials
• Generating Finite Dimensional Integrable Nonlinear Dynamical Systems
• A unification in the theory of linearization of second order nonlinear ordinary differential equations
• Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator
• On the complete integrability of a nonlinear oscillator from group theoretical perspective
• Isochronous $n$-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability
• Isochronicity conditions for some planar polynomial systems II
• Jacobi multipliers, non-local symmetries and nonlinear oscillators
• Complex Rotating Waves and Long Transients in a Ring-Network of Electrochemical Oscillators with Sparse Random Cross-Connections
• $n$-dimensional PDM-damped harmonic oscillators: Linearizability, and exact solvability
• Method of generating $N$-dimensional isochronous nonsingular Hamiltonian systems
• A class of solvable coupled nonlinear oscillators with amplitude independent frequencies