Langevin dynamics for subdiffusion with senescence effects

The phenomena of senescence are widely observed during the process of cell mitosis at the cellular level. From the perspective of statistical mechanics, the senescence can be formulated by a random walk process whose dynamic and transitional properties decay as the number of transitions increases. To explore the impact of the senescence effects on anomalous diffusion, we propose a new subordinator by adding a senescence term f(s) to the classical α-stable subordinator and then establish the subordinated Langevin equation to characterize the subdiffusion with senescence effects. By taking the senescence term f(s) in the specific form of power law, we evaluate the ensemble average and time average of the mean-squared displacements and derive the Fokker-Planck equations of the propagators. The quantitative analyses reveal different diffusion regimes for the scenarios of weak senescence and strong senescence. The results show that the strong senescence effect has a damping influence and slows down the subdiffusion, while the weak senescence effect has no impact on the subdiffusion at large-time limit. The proposed Langevin equation and the quantitative analyses provide a new perspective for studying the senescence effects in anomalous diffusion phenomena.