The linearity of the master stability function

¹ Centre for Artificial Intelligence, Chennai Institute of Technology - Chennai, India
² Centre for Nonlinear Systems, Chennai Institute of Technology - Chennai, India
³ Department of Electronics and Communications Engineering and University Centre of Research & Development, Chandigarh University - Mohali-140413, Punjab
⁴ Information Technology Collage, Imam Ja'afar Al-Sadiq University - 10001, Baghdad, Iraq
⁵ Department of Mathematics, Statistics and Physics, Qatar University - Doha 2713, Qatar

^(a) rkarthiekeyan@gmail.com, karthikeyan.rajagopal@citchennai.net (corresponding author)

Received: 17 August 2021
Accepted: 9 December 2021

Abstract

The master stability function (MSF) is a tool to evaluate the local stability of the synchronization in coupled oscillators. Computing the MSF of a network of a specific oscillator results in a curve whose shape is dependent on the nodes' dynamics, network topology, coupling function, and coupling strength. This paper calculates the MSF of networks of two diffusively coupled oscillators by considering different single variable and multi-variable couplings. Then, the linearity of the MSF is investigated by fitting a straight line to the MSF curve, and the root mean square error is obtained. It is observed that the multi-variable coupling with equal coefficients on all variables results in a linear MSF regardless of the dynamics of the nodes.