dorsal/arxiv
View SchemaAngular velocity variations and stability of spatially explicit prey-predator systems
| Authors | Refael Abta, Nadav M. Shnerb |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0612021 |
| URL | https://arxiv.org/abs/q-bio/0612021 |
| DOI | 10.1103/PhysRevE.75.051914 |
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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"abstract": "The linear instability of Lotka-Volterra orbits in the homogenous manifold of\na two-patch system is analyzed. The origin of these orbits instability in the\nabsence of prey migration is revealed to be the dependence of the angular\nvelocity on the azimuthal angle; in particular, the system desynchronizes at\nthe exit from the slow part of the trajectory. Using this insight, an analogous\nmodel of a two coupled oscillator is presented and shown to yield the same type\nof linear instability. This unables one to incorporate the linear instability\nwithin a recently presented general framework that allows for comparison of all\nknown stabilization mechanisms and for simple classification of observed\noscillations.",
"arxiv_id": "q-bio/0612021",
"authors": [
"Refael Abta",
"Nadav M. Shnerb"
],
"categories": [
"q-bio.PE",
"cond-mat.other",
"nlin.AO"
],
"doi": "10.1103/PhysRevE.75.051914",
"title": "Angular velocity variations and stability of spatially explicit prey-predator systems",
"url": "https://arxiv.org/abs/q-bio/0612021"
},
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