Active motions of Brownian particles in a generalized energy-depot model

We present a generalized energy-depot model in which the rate of conversion of the internal energy into motion can be dependent on the position and velocity of a particle. When the conversion rate is a general function of the velocity, the active particle exhibits diverse patterns of motion, including a braking mechanism and a stepping motion. The phase trajectories of the motion are investigated in a systematic way. With a particular form of the conversion rate dependent on the position and velocity, the particle shows a spontaneous oscillation characterizing a negative stiffness. These types of active behaviors are compared with similar phenomena observed in biology, such as the stepping motion of molecular motors and amplification in the hearing mechanism. Hence, our model can provide a generic understanding of the active motion related to the energy conversion and also a new control mechanism for nano-robots. We also investigate the effect of noise, especially on the stepping motion, and observe random walk-like behavior as expected.