  The apparent stability of population oscillations in ecological systems is a
long-standing puzzle. A generic solution for this problem is suggested here.
The stabilizing mechanism involves the combined effect of spatial migration,
amplitude-dependent frequency, and noise: small differences between spatial
patches, induced by the noise, are amplified by the frequency gradient.
Migration among desynchronized regions then stabilizes the oscillations in the
vicinity of the homogenous manifold. A simple model of diffusively coupled
oscillators allows the derivation of quantitative results, like the dependence
of the desynchronization upon diffusion strength and frequency differences. For
an unstable system, a noise-induced transition is demonstrated, from extinction
for small noise to stability if the noise exceeds some threshold. The coupled
oscillator model is shown to reproduce all previously suggested stabilizing
mechanisms. Accordingly, we suggest using this model as a standard tool for
identification and classification of population oscillations on spatial
domains.
