Non-linear diffusion with stochastic resetting

Resetting or restart, when applied to a stochastic process, usually brings its dynamics time-independent stationary state. In turn, the optimal resetting rate makes mean time reach target be shortest one. These and other intriguing problems have been intensively studied in case of ordinary diffusive processes over last decade. this paper we consider influence on motion modeled terms non-linear differential equation. The reason for non-linearity is power-law dependence diffusion coefficient probability density function or, another context, concentration particles. We briefly outline issue at first prepare foundations our further considerations. Then, derive an exact formula squared displacement demonstrate how it attains steady-state value under exponential resetting. This mechanism also about that spatial support function, which free confined set finite measure, tends span entire domain real numbers. addition, explore first-passage properties intermittent by find analytical expressions determine numerically minimizes needed particle pre-determined target. Finally, test confirm universal property relative fluctuation optimally restarted equal unity.