Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model
Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model
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DOI：
10.1063/1.2991108
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发表时间：
2008-12-01
期刊：
影响因子：
2.9
通讯作者：
Rabinovich, Mikhail I.
中科院分区：
文献类型：
--
作者：
Afraimovich, Valentin;Tristan, Irma;Rabinovich, Mikhail I.
预测多物种生态系统的演化是一个有趣的问题。一个具有必要预测能力的足够复杂的模型需要结构稳定的解决方案。系统参数的微小变化不应定性扰动其解决方案。当一个人只对演化的渐近结果感兴趣时（当时间到达无穷大时），那么这个问题就有了一个简单的数学图像，涉及动力系统的简单吸引子（不动点或极限环）。然而，为了准确预测演化，瞬态解的分析是至关重要的。本文在传统的Lotka-Volterra模型（在某种意义上进行了推广）的框架下，证明了多物种序贯竞争的瞬态解具有高概率的可重复性和可预测性.
Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka-Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.