论文标题
多变量相互作用人群的衰老衰老
Aging by near-extinctions in many-variable interacting populations
论文作者
论文摘要
多种物种生态系统的模型，例如Lotka-Volterra和复制器方程，表明这些系统通常显示出近乎灭绝的过程，其中人口量在一段时间内非常接近零，然后反弹，并伴随着动力学（Aging）的减速。在这里，我们通过引入一个可解决的多变量模型来调查近渗透和衰老之间的联系，其中每个人口大小的时间导数都在零时消失，并且一些有限的最大尺寸。我们表明，当种群之间进行随机相互作用时，衰老通常会出现。人口大小保持指数型（及时）与长时间的吸收值，这两个值之间的迅速过渡。衰老的机制与通常的玻璃系统中的作用不同：长期以来，该系统在不稳定的固定点附近而不是边缘固定点附近演变。
Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding, accompanied by a slowdown of the dynamics (aging). Here, we investigate the connection between near-extinction and aging by introducing an exactly solvable many-variable model, where the time derivative of each population size vanishes both at zero and some finite maximal size. We show that aging emerges generically when random interactions are taken between populations. Population sizes remain exponentially close (in time) to the absorbing values for extended periods of time, with rapid transitions between these two values. The mechanism for aging is different from the one at play in usual glassy systems: at long times, the system evolves in the vicinity of unstable fixed points rather than marginal ones.
