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

Refael Abta; Nadav M. Shnerb

doi:10.1103/physreve.75.051914

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arXiv · q-bio/0612021

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

Refael Abta·Nadav M. Shnerb

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Abstract

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.

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Refael Abta, Nadav M. Shnerb. 2006-12-12. Angular velocity variations and stability of spatially explicit prey-predator systems. https://doi.org/10.1103/physreve.75.051914

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