Effects of Amplitude, Maximal Lyapunov Exponent, and Kaplan-Yorke Dimension of Dynamical Oscillators on Master Stability Function

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.

Automated summary

Obtaining the master stability function is a well-established method for studying synchronization in networks of chaotic oscillators. This study examines the effect of oscillator dynamics on the master stability function using a flexible oscillator with adjustable parameters. The results show that the amplitude of the oscillations has no significant effect on the master stability function, but oscillators with larger maximal Lyapunov exponent require higher coupling strength for synchronization. Interestingly, there is no linear relationship between the Kaplan-Yorke dimension and the coupling strength needed for complete synchronization.