Effects of Amplitude, Maximal Lyapunov Exponent,
and Kaplan–Yorke Dimension of Dynamical Oscillators on Master
Stability Function
Mohadeseh Shafiei Kafraj and Fahimeh Nazarimehr
Department of Biomedical Engineering, Amirkabir University of
Technology (Tehran Polytechnic), Iran
Dibakar Ghosh Physics and Applied Mathematics Unit, Indian Statistical
Institute, 203 B. T. Road, Kolkata 700108, India
Karthikeyan Rajagopal Centre for Nonlinear Systems, Chennai Institute of Technology,
Chennai, India
Sajad Jafari∗ Department of Biomedical Engineering, Amirkabir University of
Technology (Tehran Polytechnic), Iran Health Technology Research
Institute, Amirkabir University of Technology (Tehran
Polytechnic), Iran sajadjafari@aut.ac.ir
J. C. Sprott Department of Physics, University of Wisconsin – Madison,
Madison, WI 53706, USA
Received July 21, 2021; Revised November 8, 2021
Obtaining the master stability function is a well-known approach to
study the synchronization in networks of chaotic oscillators. This
method considers a normalized coupling parameter which allows for a
separation of network topology and local dynamics of the nodes. The
present study aims to understand how the dynamics of oscillators
affect the master stability function. In order to examine the effect
of various characteristics of oscillators, a flexible oscillator
with adjustable amplitude, Lyapunov exponent, and Kaplan–Yorke
dimension is used. Not surprisingly, it is demonstrated that the
amplitude of the oscillations has no substantial effect on the
master stability function, i.e. the coupling strength needed for the
complete synchronization is not changed. However, the flexible
oscillators with larger maximal Lyapunov exponent synchronize with
larger coupling strength. Interestingly, it is shown that there is
no linear connection between the Kaplan–Yorke dimension and coupling
strength needed for complete synchronization.
Ref:
M. S. Kafraj, F. Nazarimehr, D. Ghosh, K. Rajagopal, S. Jafari, and
J. C. Sprott, International Journal of Bifurcation and Chaos 32,
2250067-1-8 (2022).