The paper consists of two parts: (i) the empirical one where the non-linear, long-term autocorrelations present in high-frequency data extracting from the Warsaw Stock Exchange were analyzed and (ii) theoretical one where predictions of our model (Quantitative Finance 3 (2003) 201; Physica A...

We studied random walks on two-dimensional patterns formed by the sequence of configurations of complex elementary cellular automata (CA) with random initial configurations. The walkers are allowed to jump between nearest neighbours or next nearest neighbours 1 sites. On patterns of rules 22,...

Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an inhomogeneous active region, coupled and uncoupled, respectively....

Weights of edges and nodes on food webs which are available from the empirical data hide much information about energy flows and biomass distributions in ecosystem. We define a set of variables related to weights for each species i, including the throughflow Ti, the total biomass Xi, and the...

General conditions for the appearance of the power-law distribution of total weights concentrated in vertices of complex network systems are established. By use of the rate equation approach for networks evolving by connectivity-governed attachment of every new node to p⩾1 exiting nodes and by...

We discuss the role of the initial conditions for the dynamical anomalies observed in the quasi-stationary states of the Hamiltonian mean field (HMF) model.

In recent years the interest around the study of anomalous relaxation and diffusion processes is increased due to their importance in several natural phenomena. Moreover, a further generalization has been developed by introducing time-fractional differentiation of distributed order which ranges...

A model, which describes contaminant transport in statistically homogeneous, disordered medium with sharply contrasting properties, is analyzed. At intermediate times, when there is no equilibrium between mobile and immobile contaminant fractions, the transport is described by a set of regimes...

We developed the most general Lévy walks with varying velocity, shorter called the Weierstrass walks (WW) model, by which one can describe both stationary and non-stationary stochastic time series. We considered a non-Brownian random walk where the walker moves, in general, with a velocity that...

We analyze a multidimensional nonlinear diffusion equation taking a spatial time dependent diffusion coefficient and external forces into account. We obtain new exact classes of solutions and investigate the transverse effects induced by an external force applied in the system. We also connect...