Active Ornstein-Uhlenbeck particle under stochastic resetting

We investigate the dynamics of an inertial active Ornstein-Uhlenbeck (OU) particle in the presence of stochastic resetting. Using the renewal approach, we compute the mean square displacement (MSD) and position probability distribution functions both in the overdamped and underdamped regimes. The impact of resetting and activity is significant only in the steady state. The steady state MSD gets suppressed with an increase in the resetting rate and shows a nonmonotonic impact on the duration of activity. For a very short and very long persistent duration of activity, the steady-state MSD is same as that of a passive Brownian particle. However, for an intermediate range of activity time, the steady state MSD is enhanced and shows a maximum, allowing the particle to explore a larger region, thereby increasing the probability of encountering a wide-spread target. These results are further supported by the position probability distribution function. Moreover, when the particle is suspended in a viscoelastic medium characterized by the presence of memory, the MSD interestingly develops an intermediate-time plateau and the plateau depends on the strength of viscoelasticity and viscoelastic relaxation time. An increase in viscoelasticity strength broadens the plateau and suppresses MSD. On the other hand, slower viscoelastic relaxation makes memory effects weaker, resulting in the disappearance of the plateau. Similarly, fast resetting dominates the memory effects and makes the system approach steady state faster, overcoming the intermediate plateau in MSD. Moreover, a longer relaxation time amplifies the enhancement of steady state MSD due to activity, making it a favorable condition for reaching the wide-spread target. Finally, our analytical results agree well with numerical simulation.