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 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.

Automated summary

In this paper, a method for generating nonlinear ordinary differential equations (ODEs) is proposed to describe the dynamics of nonlinear oscillators with either amplitude independent frequency or amplitude-dependent frequency. The method includes deriving the associated integrals and general solutions in harmonic form for both cases. The applicability of this method is demonstrated through examples of coupled first-order nonlinear ODEs.