  A generic aggregate forming system in two dimensions (2D) is studied using
canonical ensemble constant temperature molecular dynamics simulation. The
aggregates form due to the competition between short range attraction and long
range repulsion of pair-wise interactions. Choosing the appropriate set of
interaction parameters, we focus on characterising the collective dynamics in
two specific morphologies, {\it viz.} compact and string-like aggregates. We
focus on the temporal evolution of the mobility of an individual particle and
the dynamic change in its nearest neighbourhood, measured in terms of the
Debye-Waller factor ($\bar{u}_i^2$) and the non-affine parameter ($\chi$),
respectively (defined in the text), and their interrelation over several
lengths of observation time $\tau_w$. The distribution for both measures are
found to follow the relation: $P(x;\tau_w) \sim \tau_w^{-\gamma}x$ for the
measured quantity $x$. The exponent $\gamma$ is equal to $2$ and $1$
respectively, for the compact and string-like morphologies following the ideal
fractal dimension of these aggregates. A functional dependence between these
two observables is determined from a detailed statistical analysis of their
joint and conditional distributions. The results obtained can readily be used
and verified by experiments on aggregate forming systems such as globular
proteins, nanoparticle self-assembly etc. Further, the insights gained from
this study might be useful to understand the evolution of collective dynamics
in diverse glass-forming systems.
