  The mechanisms and properties of synchronization of oscillating ecological
populations attract attention because it is a fairly common phenomenon and
because spatial synchrony may elevate a risk of extinction and may lead to
other environmental impacts. Conditions for stable synchronization in a system
of linearly coupled predator-prey oscillators have been considered in the past.
However, the spatial dispersion coupling may be relatively weak and may not
necessarily lead to a stable, complete synchrony. If the coupling between
oscillators is too weak to induce a stable synchrony, oscillators may be
engaged into intermittent synchrony, when episodes of synchronized dynamics are
interspersed with the episodes of desynchronized dynamics. In the present study
we consider the temporal patterning of this kind of intermittent synchronized
dynamics in a system of two dispersal-coupled Rosenzweig-MacArthur
predator-prey oscillators. We consider the properties of the distributions of
durations of desynchronized intervals and their dependence on the model
parameters. We show that the temporal patterning of synchronous dynamics (an
ecological network phenomenon) may depend on the properties of individual
predator-prey patch (individual oscillator) and may vary independently of the
strength of dispersal. We also show that if the dynamics of predator is slow
relative to the dynamics of the prey (a situation that may promote brief but
large outbreaks), dispersal-coupled predator-prey oscillating populations
exhibit numerous short desynchronizations (as opposed to few long
desynchronizations) and may require weaker dispersal in order to reach strong
synchrony.
