Related papers: Dynamical systems on hypergraphs
Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a…
Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to…
Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models…
Motivated by applications to a wide range of assemble-to-order systems, operations scheduling, healthcare systems and collaborative economy applications, we introduce a stochastic matching model on hypergraphs, extending the model in [15]…
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…
Higher-order networks have emerged as a powerful framework to model complex systems and their collective behavior. Going beyond pairwise interactions, they encode structured relations among arbitrary numbers of units through representations…
From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…
We explore the dynamical behavior and energetic properties of a model of two species that interact nonlocally on finite graphs. The authors recently introduced the model in the context of nonquadratic Finslerian gradient flows on…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
The richness of many complex systems stems from the interactions among their components. The higher-order nature of these interactions, involving many units at once, and their temporal dynamics constitute crucial properties that shape the…
A broad range of dynamical systems involve multi-body interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, the Majority Rule,…
Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to…
Dynamical systems on hypergraphs can display a rich set of behaviours not observable for systems with pairwise interactions. Given a distributed dynamical system with a putative hypergraph structure, an interesting question is thus how much…
Complex networked systems in fields such as physics, biology, and social sciences often involve interactions that extend beyond simple pairwise ones. Hypergraphs serve as powerful modeling tools for describing and analyzing the intricate…
Non-dyadic higher-order interactions affect collective behavior in various networked dynamical systems. Here we discuss the properties of a novel Ising model with higher-order interactions and characterize its phase transitions between the…
Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…
Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions…
We present a simple model for describing the dynamics of the interaction between a homogeneous population or society, and the natural resources and reserves that the society needs for its survival. The model is formulated in terms of…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
Hypergraphs, capable of representing high-order interactions via hyperedges, have become a powerful tool for modeling real-world biological and social systems. Inherent relationships within these real-world systems, such as the encoding…