At first, it was just an urge to understand in what ways a complex system can synchronize. “I’m curious about how things work,” says physicist Jan Fialkowski, who recently joined the Complexity Science Hub.
However, his findings about complex dynamical networks, which have just been published in Physical Review Letters, can help us better understand the dynamics of social and biological systems.
“Having my paper accepted was a pleasant surprise,” says Fialkowski, whose paper was the result of his master’s thesis.
“In this work, we show that the synchronization of complex dynamical networks can be achieved following two very distinct paths,” explains Fialkowski. The precise description of these phenomena can help understand, for instance, the dynamics of opinions in society.
“Synchronization can be interpreted as a consensus between individuals,” points out Fialkowski. “When an idea is well accepted by the population, it can recruit more and more people until consensus is reached. If two ideas are sufficiently different, you will observe the emergence of two distinct opinions that coexist for a long time. Then it is much more difficult to reach a consensus.”
From disorder to order
In the study, Fialkowski and his colleagues found that systems of coupled oscillators exhibit little to no synchronization when weak interactions are present, since each oscillator follows its own rhythm. When the coupling strength increases, oscillators tend to behave similarly and synchronize their movements.
“Our simulations and advanced analytical methods show that the transition to synchronization can occur in two different ways: either one group of oscillators dominates and forces successively the others into synchronization, or two clusters of equal strength emerge and synchronize with each other in a sudden event,” says Fialkowski, who’s now pursuing his PhD on supply networks.
The article “Heterogeneous Nucleation in Finite-Size Adaptive Dynamical Networks” was published in Physical Review Letters.