Diffusion of Active Particles Subject both to Additive and Multiplicative Noises

We consider a Langevin equation of active Brownian motion which contains a multiplicative as well as an additive noise term. We study the dependences of the effective diffusion coefficient D_eff on both the additive and multiplicative noises. It is found that for fixed small additive noise intensity D_eff varies non−monotonously with multiplicative noise intensity, with a minimum at a moderate value of multiplicative noise, and D_eff increases monotonously, however, with the multiplicative noise intensity for relatively strong additive noise; for fixed multiplicative noise intensity D_eff decreases with growing additive noise intensity until it approaches a constant. An explanation is also given of the different behavior of D_eff as additive and multiplicative noises approach infinity, respectively.