Anomalous diffusion and fluctuations in complex systems and networks

Following significant advances in microscopic and macroscopic single-particle tracking and supercomputing, the theoretical investigation of fluctuations and anomalous dynamics in complex systems is currently of high interest. Stochastic processes and their generalizations represent an important tool for the statistical description of such systems. Modeling random walks and stochastic processes in complex systems, including complex networks and graphs, requires an interdisciplinary approach due to the different applications in various fields, such as physics, biology, chemistry, engineering, computer science, and economy. Various studies of active and passive tracer diffusion, for instance, in biological cells and in heterogeneous and porous media showed that the underlying structure of the environment has a strong effect on the particle movement, leading to anomalous dynamics due to the constrained particle motion or the variation of the local diffusion coefficient and the potential energy function. Moreover, determining optimal search strategies is central in diverse fields, from physics to computer science, from biology to robotics. In particular, random search strategies have been widely observed for animal foraging, in reaction pathways in DNA-binding proteins, in intracellular transport, etc. Furthermore, it has been shown that the resetting of the searcher to its initial position can improve the search strategy by appropriate optimal resetting rate, which results in minimizing the mean first-passage time. This Editorial is meant to serve as an Introduction to this Focus Issue in the form of a mini-review of the field.