Structure and Dynamics of Networks with Higher-Order Interactions

Sabhahit, Narayan G (2023) Structure and Dynamics of Networks with Higher-Order Interactions. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Narayan Ganapati Sabhahit (18MS030),) Thesis_18MS030.pdf - Submitted Version Restricted to Repository staff only Download (8MB)

Abstract

In the past few decades, studies on Networks have helped reveal new and deep insights into the functioning of real-world complex systems. However, network representations su↵er from a major drawback in the sense that, by definition, they are only able to incorporate pairwise interactions. However, recently, it has been revealed that system constituents interact via higher-order interactions in various Complex Systems and are essential in mechanisms leading up to fascinating phenomena. To that end, in the thesis, we make a significant push toward understanding the structure and dynamics of networks with higher-order interactions. Using tools borrowed from information theory, we put forth a method to construct a functional hypergraph from time-series data obtained from real-world complex systems. We show that the constructed hypergraph provides new information about the structure of underlying interactions that cannot be revealed by networks. Further, we study how incorporating higher-order interactions a↵ect the steady-state behavior of a system of interacting dynamical units. Specifically, we introduce higher-order interactions in the Kurmoto model and show analytically, using the self-consistency method, that the system undergoes an abrupt (de) synchronization transition. We also study how a second-order inertial term influences the synchronization profile. Taking inspiration from the earlier works by Tanaka & Lictenberg, we develop an analytical framework to predict the steady state behavior of coupled oscillator systems with inertia interacting via higherorder interactions. The system is seen to show a first-order phase transition with prolonged hysteresis. The inertia in the system is discovered to stabilize the incoherent branch while the higher-order interactions stabilize the synchronized branch.

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