Related papers: Network Dynamics with Higher-Order Interactions: C…
We study the impact of interaction of nodes in a layer of a multiplex network on the dynamical behavior and cluster synchronization of these nodes in other layers. We find that nodes interactions in one layer affects the cluster…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
The ability to achieve coordinated behavior -- engineered or emergent -- on networked systems has attracted widespread interest over several fields. This interest has led to remarkable advances in developing a theoretical understanding of…
Multiplex networks describe systems whose interactions can be of different nature, and are fundamental to understand complexity of networks beyond the framework of simple graphs. Recently it has been pointed out that restricting the…
Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these…
Synchrony patterns describe network states in which nodes of a coupled dynamical system are grouped into clusters based on synchronization between nodes. Beyond simple synchrony, synchronized clusters may also exhibit active or inactive…
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is…
Opinion dynamics is a central subject of computational social science, and various models have been developed to understand the evolution and formulation of opinions. Existing models mainly focus on opinion dynamics on graphs that only…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
This paper provides synchronization conditions for networks of nonlinear systems. The components of the network (referred to as "compartments'' in this paper) are made up of an identical interconnection of subsystems, each represented as an…
Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of…
The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel…
Dynamic systems that consist of a set of interacting elements can be abstracted as temporal networks. Recently, higher-order patterns that involve multiple interacting nodes have been found crucial to indicate domain-specific laws of…
Hypergraphs, encoding structured interactions among any number of system units, have recently proven a successful tool to describe many real-world biological and social networks. Here we propose a framework based on statistical inference to…
In this chapter, we derive and analyse models for consensus dynamics on hypergraphs. As we discuss, unless there are nonlinear node interaction functions, it is always possible to rewrite the system in terms of a new network of effective…
The dynamics of network social contagion processes such as opinion formation and epidemic spreading are often mediated by interactions between multiple nodes. Previous results have shown that these higher-order interactions can profoundly…
The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…
Synchronization has been the subject of intense research during decades mainly focused on determining the structural and dynamical conditions driving a set of interacting units to a coherent state globally stable. However, little attention…
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…