A class of isochronous and non-isochronous nonlinear oscillators

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 osc...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Special topics, 2022-07, Vol.231 (11-12), p.2387-2399
Main Authors: Parkavi, J. Ramya, Mohanasubha, R., Chandrasekar, V. K., Senthilvelan, M., Lakshmanan, M.
Format: Article
Language:English
Subjects:
Amplitudes
Atomic
Bifurcation Delay and Multi Stability in Complex Nonlinear Systems
Bursting Oscillations
Classical and Continuum Physics
Condensed Matter Physics
Harmonic oscillators
Integrals
Materials Science
Measurement Science and Instrumentation
Molecular
Nonlinear differential equations
Nonlinear dynamics
Optical and Plasma Physics
Oscillations
Physics
Physics and Astronomy
Regular Article
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Summary: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 2 N coupled first-order nonlinear ODEs in both the cases. Further, we illustrate the theory with an example in each case.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjs/s11734-022-00484-y