Stochastic resetting of a population of random walks with resetting-rate-dependent diffusivity

We consider the problem of diffusion with stochastic resetting in a population random walks where coefficient is not constant, but behaves as power-law average rate population. Resetting occurs only beyond threshold distance from origin. This motivated by physical realizations like soft matter under shear, walk induced events other walks. first reformulate broader context so-called H\'ebraud-Lequeux model for plasticity dense matter, which diffusivity proportional to rate. Depending on parameter values, response weak external field may be either linear or non-linear non-zero position vanishing applied field, and transition between these two regimes interpreted continuous phase transition. Extending considering general relation rate, we notably find discontinuous finite small limit.