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 enables 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.
Abta
Refael
R
Department of Physics, Bar-Ilan University, Ramat-Gan, Israel.
Shnerb
Nadav M
NM
D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D006801:Humans; D007700:Kinetics; D008954:Models, Biological; D011156:Population Density; D011157:Population Dynamics; D011158:Population Growth; D011235:Predatory Behavior / Q000502:physiology*