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).

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