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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…

Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological…

In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…

Biological networks are customarily described as structurally robust. This means that they often function extremely well under large forms of perturbations affecting both the concentrations and the kinetic parameters. In order to explain…

We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits…

The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing…

We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…

The ability of groups to make accurate collective decisions depends on a complex interplay of various factors, such as prior information, biases, social influence, and the structure of the interaction network. Here, we investigate a spin…

We study the classical dynamics of resonantly modulated large-spin systems in a strong magnetic field. We show that these systems have special symmetry. It leads to characteristic nonlinear effects. They include abrupt switching between…

Tipping elements in the Earth System receive increased scientific attention over the recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element…

A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how…

In this paper, we will study the statistical behaviors of orbits. Firstly, we will show that for a dynamical systems have the shadowing property or almost specification property, the set of nonrecurrent points has full topological entropy.…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given…

Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…

Multistability-induced hysteresis has been widely studied in mechanical systems, but such behavior has proven more difficult to reproduce experimentally in flow networks. Natural flow networks like animal and plant vasculature can exhibit…

Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…

Realistic large-scale networks display an heterogeneous distribution of connectivity weights, that might also randomly vary in time. We show that depending on the level of heterogeneity in the connectivity coefficients, different…

Nonlinear systems possessing nonattracting chaotic sets, such as chaotic saddles, embedded in their state space may oscillate chaotically for a transient time before eventually transitioning into some stable attractor. We show that these…