  In this work, we study the dynamics of a single active Brownian particle and
the collective behavior of interacting active particles in evolving
heterogeneous media. We apply the idea of the diffusing diffusivity model to
mimic the environmental heterogeneity in the equation of motion of the active
particle via time-dependent activity and diffusivities. In our model, the
fluctuations of environment simultaneously and similarly affect the motility
and diffusion coefficients. We obtain the probability distribution function of
particle displacement and its moments analytically and support our data via
particle-based simulations. We finally investigate the impact of the introduced
fluctuations on the collective behavior of active Brownian particles. Our
results show that these fluctuations hinder the motility-induced phase
separation, together with a significant change of the density dependence of
particle velocities.
