We review theoretical models of individual motility as well as collective dynamics and
pattern formation of active particles. We focus on simple models of active dynamics with a …

Active matter encompasses systems whose individual constituents dissipate energy to exert
propelling forces on their environment. These systems exhibit dynamical phenomena with …

Since the subject of traffic dynamics has captured the interest of physicists, many surprising
effects have been revealed and explained. Some of the questions now understood are the …

We present an improved and enlarged version of our book Nonlinear-namics of Chaotic and
Stochastic Systems published by Springer in 2002. Basically, the new edition of the book …

When we contemplate phenomena as diverse as electrochemical deposition or the spatial
patterns of urban development, it is natural to assume that they havenothing incommon …

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian
process with a power-law time dependent diffusion coefficient. Its mean squared …

Over the past one hundred years, Brownian motion theory has contributed substantially to
our understanding of various microscopic phenomena. Originally proposed as a …

We study a model of Brownian particles which are pumped with energy by means of a non-
linear friction function, for which different types are discussed. A suitable expression for a …

We study phase transitions in models of opinion formation which are based on the social
impact theory. Two different models are discussed:(i) a cellular-automata-based model of a …

Active systems are self-driven systems that live, or function, far from thermodynamic
equilibrium. A paradigmatic example is provided by a suspension of interacting self-motile …