Comb Model With Non-Static Stochastic Resetting And Anomalous Diffusion

Nowadays, the stochastic resetting process is an attractive research topic in stochastic process. At the same time, a series of researches on stochastic diffusion in complex structures introduced ways to understand the anomalous diffusion in complex systems. In this work, we propose a non-static stochastic resetting model in the context of comb structure that consists of a structure formed by backbone inxaxis and branches inyaxis. Then, we find the exact analytical solutions for marginal distribution concerningxandyaxis. Moreover, we show the time evolution behavior to mean square displacements (MSD) in both directions. As a consequence, the model revels that until the system reaches the equilibrium, i.e., constant MSD, there is a Brownian diffusion inydirection, i.e., <(Delta y)(2)> proportional to t, and a crossover between sub and ballistic diffusion behaviors in x direction, i.e., <(Delta x)(2)> proportional to t(1/2) and <(Delta x)(2)> proportional to t(2) respectively. For static stochastic resetting, the ballistic regime vanishes. Also, we consider the idealized model according to the memory kernels to investigate the exponential and tempered power-law memory kernels effects on diffusive behaviors. In this way, we expose a rich class of anomalous diffusion process with crossovers among them. The proposal and the techniques applied in this work are useful to describe random walkers with non-static stochastic resetting on comb structure.