arXiv subjects

Refael Abta

Publications and source records attributed to Refael Abta.

3 recordsLinked to original sources

arXiv2007

Desynchronization and sustainability of noisy metapopulation cycles

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.

q-bio.PE↗

arXiv2006

Angular velocity variations and stability of spatially explicit prey-predator systems

The linear instability of Lotka-Volterra orbits in the homogenous manifold of a two-patch system is analyzed. The origin of these orbits instability in the absence of prey migration is revealed to be the dependence of the angular velocity on the azimuthal angle; in particular, the system desynchronizes at the exit from the slow part of the trajectory. Using this insight, an analogous model of a two coupled oscillator is presented and shown to yield the same type of linear instability. This unables one to incorporate the linear instability within a recently presented general framework that allows for comparison of all known stabilization mechanisms and for simple classification of observed oscillations.

q-bio.PE↗

arXiv2006

Amplitude dependent frequency, desynchronization, and stabilization in noisy metapopulation dynamics

The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that the combined effects of migration and noise cannot account for the stabilization. The missing ingredient is the dependence of the oscillations' frequency upon their amplitude; with that, noise-induced differences between patches are amplified due to the frequency gradient. Migration among desynchronized regions then stabilizes a "soft" limit cycle in the vicinity of the homogenous manifold. A simple model of diffusively coupled oscillators allows the derivation of quantitative results, like the functional dependence of the desynchronization upon diffusion strength and frequency differences. The oscillations' amplitude is shown to be (almost) noise independent. The results are compared with a numerical integration of the marginally stable Lotka-Volterra equations. An unstable system is extinction-prone for small noise, but stabilizes at larger noise intensity.

cond-mat.soft↗