Related papers: Do Small Worlds Synchronize Fastest?
In this paper we consider spatial networks that realize a balance between an infrastructure cost (the cost of wire needed to connect the network in space) and communication efficiency, measured by average shortest pathlength. A global…
Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…
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…
Being fundamentally a non-equilibrium process, synchronization comes with unavoidable energy costs and has to be maintained under the constraint of limited resources. Such resource constraints are often reflected as a finite coupling budget…
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the…
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,…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
Qualitatively, some real networks in the brain could be characterized as 'small worlds', in the sense that the structure of their connections is intermediate between the extremes of an orderly geometric arrangement and of a…
We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a…
Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such…
In a generalized framework, where multi-state and inter-state linkages are allowed, we derive a sufficient condition for the stability of synchronization in a network of chaotic attractors. This condition explicitly relates the network…
Cooperation is commonly found in ecological and social systems even when it apparently seems that individuals can benefit from selfish behavior. We investigate how cooperation emerges with the spatial prisoner's dilemma played in a class of…
Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics…
In this paper we study synchronized motions in complex networks in which there are distinct groups of nodes where the dynamical systems on each node within a group are the same but are different for nodes in different groups. Both…
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators…
Many real life networks, such as the World Wide Web, transportation systems, biological or social networks, achieve both a strong local clustering (nodes have many mutual neighbors) and a small diameter (maximum distance between any two…
We investigate the spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections. While strictly nearest neighbour coupling never allows spatiotemporal synchronization in our…
We propose that clusters interconnected with network topologies having minimal mean path length will increase their overall performance for a variety of applications. We approach our heuristic by constructing clusters of up to 36 nodes…
This work analyzes the problem of community structure in real-world networks based on the synchronization of nonidentical coupled chaotic R\"{o}ssler oscillators each one characterized by a defined natural frequency, and coupled according…
In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others…