Related papers: Dynamics of Coupled Maps in Heterogeneous Random N…
One of the famous results of network science states that networks with heterogeneous connectivity are more susceptible to epidemic spreading than their more homogeneous counterparts. In particular, in networks of identical nodes it has been…
Relationships between individuals in a social network, genes in biological systems, and spins in magnetic systems often reflect a mixture of positive (friendly) and negative (antagonistic) interactions. However, most studies of complex…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
In this paper, we introduce ergodic sets, subsets of nodes of the networks that are dynamically disjoint from the rest of the network (i.e. that can never be reached or left following to the network dynamics). We connect their definition to…
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be…
Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from…
We study the emerging large-scale structures in networks subject to selective pressures that simultaneously drive towards higher modularity and robustness against random failures. We construct maximum-entropy null models that isolate the…
The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…
The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals…
Using a generalized random recurrent neural network model, and by extending our recently developed mean-field approach [J. Aljadeff, M. Stern, T. Sharpee, Phys. Rev. Lett. 114, 088101 (2015)], we study the relationship between the network…
Algorithms and dynamics over networks often involve randomization, and randomization may result in oscillating dynamics which fail to converge in a deterministic sense. In this paper, we observe this undesired feature in three applications,…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long range…
Complex systems are high-dimensional nonlinear dynamical systems with intricate interactions among their constituents. To make interpretable predictions about their large-scale behavior, it is typically assumed, without a clear statement,…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…