  Lateral inhibition resulting from a double-negative feedback loop underlies
the assignment of different fates to cells in many developmental processes.
Previous studies have shown that the presence of time delays in models of
lateral inhibition can result in significant oscillatory transients before
patterned steady states are reached. We study the impact of local feedback
loops in a model of lateral inhibition based on the Notch signalling pathway,
elucidating the roles of intracellular and intercellular delays in controlling
the overall system behaviour. The model exhibits both in-phase and out-of-phase
oscillatory modes, and oscillation death. Interactions between oscillatory
modes can generate complex behaviours such as intermittent oscillations. Our
results provide a framework for exploring the recent observation of transient
Notch pathway oscillations during fate assignment in vertebrate neurogenesis.
