Related papers: Network constraints in scale free dynamical system…
Recent studies on the complex systems have shown that the synchronization of oscillators including neuronal ones is faster, stronger, and more efficient in the small-world networks than in the regular or the random networks, and many…
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…
The effects of free surfaces on the dynamic critical behavior of isotropic Heisenberg ferromagnets are studied via phenomenological scaling theory, field-theoretic renormalization group tools, and high-precision computer simulations. An…
We investigate the contact process on four different types of scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where each potential edge is updated with a rate depending on the strength of the adjacent…
Criticality has been proposed as a key principle underlying complex behavior in biological and artificial systems; however, how criticality translates from individual dynamics to collective behavior remains unclear. We study this question…
We study a simple model for a neuron function in a collective brain system. The neural network is composed of uncorrelated random scale-free network for eliminating the degree correlation of dynamical processes. The interaction of neurons…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
Critical phenomena on scale-free networks with a degree distribution $p_k \sim k^{-\lambda}$ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify…
Real-world growth processes and scalings have been broadly categorized into three growth regimes with distinctly different properties and driving forces. The first two are characterized by a positive and constant feedback between growth and…
We study the behavior of scale-free networks, having connectivity distribution P(k) k^-a, close to the percolation threshold. We show that for networks with 3<a<4, known to undergo a transition at a finite threshold of dilution, the…
Very often, when studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree-degree correlations are not present. However, simple constraints, such as the absence of multiple edges and…
How does the shape of a network change as its size increases? Although random graph models provide some expectations for such "scaling behaviors" in the structure of networks, relatively little is known about how empirical network structure…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…
The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability $q$ in…
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…
We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…