  We propose an alternative to the standard mechanisms for the formation of
rogue waves in a non-conservative, nonlinear lattice dynamical system. We
consider an ODE system that features regular periodic bursting arising from
forced symmetry breaking. We then connect such potentially exploding units via
a diffusive lattice coupling and investigate the resulting spatio-temporal
dynamics for different types of initial conditions (localized or extended). We
find that in both cases, particular oscillators undergo extremely fast and
large amplitude excursions, resembling a rogue wave burst. Furthermore, the
probability distribution of different amplitudes exhibits bimodality, with
peaks at both vanishing and very large amplitude. While this phenomenology
arises over a range of coupling strengths, for large values thereof the system
eventually synchronizes and the above phenomenology is suppressed. We use both
distributed (such as a synchronization order parameter) and individual
oscillator diagnostics to monitor the dynamics and identify potential
precursors to large amplitude excursions. We also examine similar behavior with
amplitude-dependent diffusive coupling.
