Abstract

It has become clear that anomalous diffusion is as widespread and important as normal diffusion. However, in biological systems anomalous diffusion is usually observed as a transient before transition to normal diffusion. In my talk I will describe an approach to non-linear and non-Markovian generalization of two popular models of anomalous diffusion: subdiffusive continuous time random walk and superdiffusive Levy walk model. This approach easily allows to take into account external forces and interactions between random walkers. More importantly, we show that external forces and interactions lead to the transition to seemingly normal diffusion. This may lead to a wrong conclusion in analyses of experimental results on transient subdiffusion. Contrary to normal diffusion, the properties of the process remain to depend on anomalous exponent.