Reduction of oscillator dynamics on complex networks to dynamics on complete graphs through virtual frequencies
Jian Gao1, Konstantinos Efstathiou2
1Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence, University of Groningen, P.O. Box 407, 9700 AK, Groningen, The Netherlands.
Abstract:
We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual frequencies we show that Kuramoto oscillators on annealed networks, with or without frequency-degree correlation, and Kuramoto oscillators on complete graphs with frequency-weighted coupling can be transformed to Kuramoto oscillators on complete graphs with a rearranged, virtual frequency distribution and uniform coupling. The virtual frequency distribution encodes both the natural frequency distribution (dynamics) and the degree distribution (topology). We apply this transformation to give direct explanations to a variety of phenomena that have been observed in complex networks, such as explosive synchronization and vanishing synchronization onset.
Related Concept Videos
Damped Oscillations
Although friction and other non-conservative...
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
Oscillations In An LC Circuit
Frequency Response of a Circuit
The transfer function is pivotal in characterizing how these circuits react to various frequencies, facilitating a profound understanding of their behavior. An essential parameter is the time constant, signifying the...
Network Function of a Circuit
Oscillations about an Equilibrium Position


