期刊
PHYSICAL REVIEW E
卷 83, 期 5, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.83.051108
关键词
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资金
- US National Science Foundation [DMR-0705152, DMR-0904999, DMR-1005417]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1005417] Funding Source: National Science Foundation
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [0904999] Funding Source: National Science Foundation
Population dynamics in systems composed of cyclically competing species has been of increasing interest recently. Here we investigate a system with four or more species. Using mean field theory, we study in detail the trajectories in configuration space of the population fractions. We discover a variety of orbits, shaped like saddles, spirals, and straight lines. Many of their properties are found explicitly. Most remarkably, we identify a collective variable that evolves simply as an exponential: Q proportional to e(lambda t), where lambda is a function of the reaction rates. It provides information on the state of the system for late times (as well as for t -> -infinity). We discuss implications of these results for the evolution of a finite, stochastic system. A generalization to an arbitrary number of cyclically competing species yields valuable insights into universal properties of such systems.
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