https://doi.org/10.1140/epjs/s11734-022-00484-y
Regular Article
A class of isochronous and non-isochronous nonlinear oscillators
1
Centre for Nonlinear Science and Engineering, School of Electrical and Electronics Engineering, SASTRA Deemed University, 613401, Thanjavur, Tamil Nadu, India
2
Centre for Nonlinear Systems, Chennai Institute of Technology, 600069, Chennai, Tamil Nadu, India
3
School of Electrical and Electronics Engineering, Centre for Nonlinear Science and Engineering, SASTRA University, 613401, Thanjavur, Tamil Nadu, India
4
Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, 620024, Tiruchirappalli, Tamil Nadu, India
Received:
22
October
2021
Accepted:
16
February
2022
Published online:
5
March
2022
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.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2022
