  Numerical simulations are performed on the collective dynamics of active
disks, whose self-propulsion speed ($U$) varies in time, and whose orientation
evolves according to rotational Brownian motion. Two protocols for the
evolution of speed are considered: (i) a deterministic one involving a periodic
change in $U$ at a frequency $\omega$; and (ii) a stochastic one in which the
speeds are drawn from a power-law distribution at time-intervals governed by a
Poissonian process of rate $\beta$. In the first case, an increase in $\omega$
causes the disks to go from a clustered state to a homogeneous one through an
apparent phase-transition, provided that the direction of self-propulsion is
allowed to reverse. Similarly, in the second case, for a fixed value of
$\beta$, the extent of cluster-breakup is larger when reversals in the
self-propulsion direction are permitted. Motility-induced phase separation of
the disks may therefore be avoided in active matter suspensions in which the
constituents are allowed to reverse their self-propulsion direction, immaterial
of the precise temporal nature of the reversal (deterministic or stochastic).
Equally, our results demonstrate that phase separation could occur even in the
absence of a time-averaged motility of an individual active agent, provided
that the rate of direction reversals is smaller than the orientational
diffusion rate.
