竞争性无序动力系统中的复杂性-稳定性关系
Complexity-stability relationships in competitive disordered dynamical systems
AI总结：
本文基于竞争性Lotka-Volterra模型的非线性推广，重新审视May的复杂性-稳定性论断，发现无序动力系统中复杂性既可去稳定化也可稳定化，取决于自相互作用与交叉相互作用的相对增长速率。
摘要：
罗伯特·梅曾著名地利用随机矩阵理论预测，大型复杂系统无法容纳稳定的不动点。然而，这一普遍结论并不总是得到经验观察的支持：从细胞到生物群系，生物系统规模庞大、结构复杂，且往往保持稳定。在本文中，我们结合生态学与随机矩阵理论的最新进展，重新审视梅的论证。我们聚焦于竞争性系统，并利用竞争性Lotka-Volterra模型的非线性推广，表明在无序动力系统中实际上存在两种复杂性-稳定性关系：若自相互作用随密度的增长快于交叉相互作用，则复杂性具有去稳定化作用；但若交叉相互作用的增长快于自相互作用，则复杂性具有稳定化作用。
英文摘要：
Robert May famously used random matrix theory to predict that large, complex systems cannot admit stable fixed points. However, this general conclusion is not always supported by empirical observation: from cells to biomes, biological systems are large, complex, and often stable. In this paper, we revisit May's argument in light of recent developments in both ecology and random matrix theory. We focus on competitive systems, and, using a nonlinear generalization of the competitive Lotka-Volterra model, we show that there are, in fact, two kinds of complexity-stability relationships in disordered dynamical systems: if self-interactions grow faster with density than cross-interactions, complexity is destabilizing; but if cross-interactions grow faster than self-interactions, complexity is stabilizing.
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