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 Deff on both the additive and multiplicative noises. It is found that for fixed small additive noise intensity Deff varies non-monotonously with multiplicative noise intensity, with a minimum at a moderate value of multiplicative noise, and Deff increases monotonously, however, with the multiplicative noise intensity for relatively strong additive noise; for fixed multiplicative noise intensity Deff decreases with growing additive noise intensity until it approaches a constant. An explanation is also given of the different behavior of Deff as additive and multiplicative noises approach infinity, respectively.