  We examine a model of two interacting populations of phase oscillators
labelled `Blue' and `Red'. To this we apply tempered stable L\'{e}vy noise, a
generalisation of Gaussian noise where the heaviness of the tails parametrised
by a power law exponent $\alpha$ can be controlled by a tempering parameter
$\lambda$. This system models competitive dynamics, where each population seeks
both internal phase synchronisation and a phase advantage with respect to the
other population, subject to exogenous stochastic shocks. We study the system
from an analytic and numerical point of view to understand how the phase lag
values and the shape of the noise distribution can lead to steady or noisy
behaviour. Comparing the analytic and numerical studies shows that the bulk
behaviour of the system can be effectively described by dynamics in the
presence of tilted ratchet potentials. Generally, changes in $\alpha$ away from
the Gaussian noise limit, $1< \alpha < 2$, disrupts the locking between Blue
and Red, while increasing $\lambda$ acts to restore it. However we observe that
with further decreases of $\alpha$ to small values, $\alpha\ll 1$, with
$\lambda\neq 0$, locking between Blue and Red may be restored. This is seen
analytically in a restoration of metastability through the ratchet mechanism,
and numerically in transitions between periodic and noisy regions in a fitness
landscape using a measure of noise. This non-monotonic transition back to an
ordered regime is surprising for a linear variation of a parameter such as the
power law exponent and provides a novel mechanism for guiding the collective
behaviour of such a complex competitive dynamical system.
