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Recent researches on complex systems highlighted the so-called super-linear growth phenomenon. As the system size $P$ measured as population in cities or active users in online communities increases, the total activities $X$ measured as GDP…
We introduce a non-growth model that generates the power-law distribution with the Zipf exponent. There are N elements, each of which is characterized by a quantity, and at each time step these quantities are redistributed through binary…
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…
This article is a short review of the recent results on properties of nonlinear fractional maps which are maps with power- or asymptotically power-law memory. These maps demonstrate the new type of attractors - cascade of bifurcations type…
Power-law probability distributions are widely used to model extreme statistical events in complex systems, with applications to a vast array of natural phenomena ranging from earthquakes to stock market crashes to pandemics. We show that…
We develop a ``unified'' model that describes both ``micro'' and ``macro'' evolutions within a single theoretical framework. The eco-system is described as a dynamic network; the population dynamics at each node of this network describes…
How are people linked in a highly connected society? Since in many networks a power-law (scale-free) node-degree distribution can be observed, power-law might be seen as a universal characteristics of networks. But this study of…
Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…
This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach…
We analyze the fine-grained connections between the average degree and the power-law degree distribution exponent in growing information networks. Our starting observation is a power-law degree distribution with a decreasing exponent and…
Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual…
We study the emergence of a power law distribution in the systems which can be characterized by a hierarchically organized supplying network. It is shown that conservation laws on the branches of the network can, at some approximation,…
We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with…
We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be…
Trajectories of units moving on networks are relevant for nonlinear dynamical systems as diverse as polymers, ocean drifters, and human mobility. Although RQA is a well-researched tool with applications in many areas, it has rarely been…
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables…
The concept of emergence is a powerful concept to explain very complex behaviour by simple underling rules. Existing approaches of producing emergent collective behaviour have many limitations making them unable to account for the…