Modeling multiple anomalous diffusion behaviors on comb-like structures

In this work, a generalized comb model which includes the memory kernels and linear reactions with irreversible and reversible parts are introduced to describe complex anomalous diffusion behavior. The probability density function (PDF) and the mean squared displacement (MSD) are obtained by analytical methods. Three different physical models are studied according to different reaction processes. When no reactions take place, we extend the diffusion process in 1-D under stochastic resetting to the N-D comb-like structures with backbone resetting and global resetting by using physically derived memory kernels. We find that the two different resetting ways only affect the asymptotic behavior of MSD in the long time. For the irreversible reaction, we obtain memory kernels based on experimental evidence of the transport of inert particles in spiny dendrites and explore the front propagation of CaMKII along dendrites. The reversible reaction plays an important role in the intermediate time, but the asymptotic behavior of MSD is the same with that in case of no reaction terms. The proposed reaction-diffusion model on the comb structure provides a generalized method for further study of various anomalous diffusion problems.