  We develop a reduced model for the slow unsteady dynamics of an isotropic
chemically active particle near the threshold for spontaneous motion. Building
on the steady theory developed in part I of this series, we match a weakly
nonlinear expansion valid on the particle scale with a leading-order
approximation in a larger-scale unsteady remote region, where the particle acts
as a moving point source of diffusing concentration. The resulting amplitude
equation for the velocity of the particle includes a term representing the
interaction of the particle with its own concentration wake in the remote
region, which can be expressed as a time integral over the history of the
particle motion, allowing efficient simulation and theoretical analysis of
fully three-dimensional unsteady problems. To illustrate how to use the model,
we study the effects of a weak force acting on the particle, including the
stability of the steady states and how the velocity vector realigns towards the
stable one, neither of which previous axisymmetric and steady models were able
to capture. This unsteady formulation could also be applied to most of the
other perturbation scenarios studied in part I as well as the dynamics of
interacting active particles.
