Analysis of the non-stationary model of coupled oscillators with inductive coupling

TL;DR

This paper investigates a non-stationary model of inductively coupled oscillators, deriving explicit second derivative expressions using difference equations to facilitate numerical analysis of their dynamics.

Contribution

It introduces a method based on difference equations to obtain explicit second derivatives for inductively coupled oscillators, aiding numerical simulations.

Findings

Derived explicit second derivative expressions for inductive coupling

Analyzed the effectiveness of the difference equations method

Provided insights into the dynamics of non-stationary coupled oscillators

Abstract

The model of coupled oscillators plays an important role in modern physics. It is used for description of various processes: from vibrations atoms in solid states to electromagnetic oscillations in slow-wave structures. The model with short-range coupling is the most widely used, for which a separate oscillator is coupled with two adjacent ones only. There are two main types of oscillators coupling: capacitive (electric, power) and inductive (magnetic, inertial). In the first case, the coupling is proportional to the amplitudes of oscillations in the adjacent cells, in the second one - to the second derivative of these amplitudes. For numerical study of dynamics of a system that can be described by a model of coupled oscillators with an inductive coupling, it is necessary to find explicit expressions for the second derivatives of the amplitudes. To find these expressions, we propose to use the method that is based on the solution of difference equations. The results of the analysis of this method are given in the paper.