Related papers: Coupled networks and networks with bimodal frequen…

We consider the coupling between two networks, each having N nodes whose individual dynamics is modeled by a two-state master equation. The intra-network interactions are all to all, whereas the inter-network interactions involve only a…

We consider a population of two-dimensional oscillators with random couplings, and explore the collective states. The coupling strength between oscillators is randomly quenched with two values one of which is positive while the other is…

We consider ensembles of sine-coupled phase oscillators consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble…

Overrepresentation of bidirectional connections in local cortical networks has been repeatedly reported and is in the focus of the ongoing discussion of non-random connectivity. Here we show in a brief mathematical analysis that in a…

In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…

We study optimal synchronization in networks of heterogeneous phase oscillators. Our main result is the derivation of a synchrony alignment function that encodes the interplay between network structure and oscillators' frequencies and can…

Synchronization among rhythmic elements is modeled by coupled phase-oscillators each of which has the so-called natural frequency. A symmetric natural frequency distribution induces a continuous or discontinuous synchronization transition…

The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on…

We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…

We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…

We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…

We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the…

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling…

Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…

This paper concerns the reliability of a pair of coupled oscillators in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations regardless of the network's initial…

In continuation of prior work, we investigate ties between a network's connectivity and ensemble dynamics. This relationship is notoriously difficult to approach mathematically in natural, complex networks. In our work, we aim to understand…

Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…

Complex networks are a successful framework to describe collective behaviour in many applications, but a notable gap remains in the current literature, that of proving asymptotic convergence in networks of piecewise-smooth systems. Indeed,…

Populations of globally coupled identical maps subject to additive, independent noise are studied in the regimes of strong coupling. Contrary to each noisy population element, the mean field dynamics undergoes qualitative changes when the…

Consensus algorithms on networks have received increasing attention in recent years for various applications ranging from animal flocking to multi-vehicle co-ordination. Building on the established model for second-order consensus of…