论文标题
随机Lotka-Volterra模型的平衡和玻璃阶段的特性
Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise
论文作者
论文摘要
在这封信中，我们研究了理论生态学中的参考模型，即在存在有限的人口噪声的情况下，无序的生态社区的Lotka-Volterra模型。我们的理论分析利用映射到平衡障碍系统的优势，证明，对于足够的异质相互作用和低人口统计学噪声，系统显示了多个平衡阶段，我们已经充分表征了。特别是，我们表明在这个阶段，稳定的平衡数在物种数量中是指数的。在进一步降低人口噪声后，我们将“ gardner”过渡到一个边缘稳定的阶段，类似于在无定形材料中观察到的阶段。我们通过数值模拟确认并补充了我们的分析结果。此外，我们通过证明他们对其他人相互作用的随机动力学系统（例如随机复制模型）来扩展其相关性。最后，我们讨论了它们扩展到不对称耦合的情况。
In this letter we study a reference model in theoretical ecology, the disordered Lotka-Volterra model for ecological communities, in the presence of finite demographic noise. Our theoretical analysis, which takes advantage of a mapping to an equilibrium disordered system, proves that for sufficiently heterogeneous interactions and low demographic noise the system displays a multiple equilibria phase, which we fully characterize. In particular, we show that in this phase the number of stable equilibria is exponential in the number of species. Upon further decreasing the demographic noise, we unveil a "Gardner" transition to a marginally stable phase, similar to that observed in jamming of amorphous materials. We confirm and complement our analytical results by numerical simulations. Furthermore, we extend their relevance by showing that they hold for others interacting random dynamical systems, such as the Random Replicant Model. Finally, we discuss their extension to the case of asymmetric couplings.
