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The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
We study the intrinsic properties of attractors in the Boolean dynamics in complex network with scale-free topology, comparing with those of the so-called random Kauffman networks. We have numerically investigated the frozen and relevant…
One of the defining features of active nematics is that above a critical activity the quiescent state becomes unstable to a distorted, flowing one. We show that spatial variations in activity can fundamentally change the nature of this…
We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the…
A network with local dynamics of logistic type is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small the dynamics is dissipated and there is no activity: the…
The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the…
When two periodic potentials compete in materials, one may adopt the other, which straightforwardly generates topological defects. Of particular interest are domain walls in charge-, dipole-, and spin-ordered systems, which govern…
As few real systems comprise indistinguishable units, diversity is a hallmark of nature. Diversity among interacting units shapes properties of collective behavior such as synchronization and information transmission. However, the benefits…
In citation networks, the activity of papers usually decreases with age and dormant papers may be discovered and become fashionable again. To model this phenomenon, a competition mechanism is suggested which incorporates two factors:…
Link weight is crucial in weighted complex networks. It provides additional dimension for describing and adjusting the properties of networks. The topological role of weight is studied by the effects of random redistribution of link weights…
We study an influence network of voters subjected to correlated disordered external perturbations, and solve the dynamical equations exactly for fully connected networks. The model has a critical phase transition between disordered unimodal…
We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
We introduce a model for the dynamic self-organization of the electric grid. The model is characterized by a conserved magnitude, energy, that can travel following the links of the network to satisfy nodes' load. The load fluctuates in time…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
We investigate the equilibria of a random model network exhibiting extensive chaos. In this regime, a large number of equilibria is present. They are all saddles with low-dimensional unstable manifolds. Surprisingly, despite network's…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the…
Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of…
Natural, social, and artificial multi-agent systems usually operate in dynamic environments, where the ability to respond to changing circumstances is a crucial feature. An effective collective response requires suitable information…