ABSTRACT / In the past decades, many complex systems, either natural, social, or artificial, have been modeled as networks of coupled dynamical systems, with the links describing interactions among couples of units. However, recent evidence shows that various systems are characterized by many-body, group interactions, that cannot be captured by a network description. In the last few years, a vast literature aimed at understanding how these higher-order interactions influence the global behavior of coupled systems has raised. In this talk, I will show how to develop a general theory for studying the collective behavior of coupled dynamical systems in presence of higher-order interactions. I will focus on two relevant phenomena, namely the synchronization of chaotic oscillators and formation of patterns in reaction-diffusion systems. I will introduce a mathematical formalism to describe coupled dynamics in a general framework, and I will show that it can be used to describe both phenomena under study, enabling the derivation of the necessary conditions for their onset. Finally, I will present a few results regarding my ongoing research on temporal properties of higher-order networks.
BIO / Luca Gallo is a Postdoctoral Fellow at the Department of Network and Data Science at the Central European University. He received a bachelor’s degree in physics in 2016, and a master’s degree in physics of complex systems in 2019, both from the University of Turin. He received a PhD in complex systems for physical, socio-economic and life sciences in 2022, from the University of Catania. His research interests include dynamical systems, complex networks, higher-order networks, and their applications.