The Internet is one of the largest and most complex communication and information exchange networks ever created. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for years. This paper...

In the last three years, we have witnessed an increasing number of complex network models based on a 'fractal' approach, in which parts of the network are repeatedly replaced by a given pattern. Our focus is on models that can be defined by repeatedly adding a pattern network to selected edges,...

В статье обоснована целесообразность использования фрактального моделирования процесса возникновения и распространения инноваций на предприятиях АПК;...

В статье рассматривается современная гипотеза отрыва финансового сектора экономики от реального сектора, раскрываются его причины и последствия,...

Following the thermodynamic formulation of a multifractal measure that was shown to enable the detection of large fluctuations at an early stage, here we propose a new index which permits us to distinguish events like financial crises in real time. We calculate the partition function from which...

It has been recently noticed that time series of returns in stock markets are of multifractal (multiscaling) character. In that context, multifractality has been always evidenced by its statistical signature (i.e., the scaling exponents associated to a related variable). However, a direct...

The attractor in usual box-counting methods is partitioned with a fixed grid. We describe an algorithm whose boxes can move into the phase space and adapt to the geometry of the attractor. Lyapunov exponents and the singularity spectrum from time series are estimated using this algorithm.

Random populations represented by stochastically scattered collections of real-valued points are abundant across many fields of science. Fractality, in the context of random populations, is conventionally associated with a Paretian distribution of the population's values.