论文标题
大型复杂系统中的非线性产生的弹性
Nonlinearity-generated Resilience in Large Complex Systems
论文作者
论文摘要
我们考虑了5月1972年模型的通用非线性扩展，通过在所选固定点（放置在原点）的扩展中包括随机高斯系数。随后的分析表明，只要原点保持稳定，它就会被“弹性差距”包围：半径为r*> 0之内没有其他固定点，因此，与r*相比，系统有望与典型的初始位移具有弹性。半径r*显示在与原点失去局部稳定性的相同阈值下消失，从而揭示了一种机制，该机制通过该机制，靠近临界点的系统变得越来越少。我们还发现，除了弹性半径之外，围绕原始平衡点的球中的固定点的数量呈指数增长，从而使系统动力学对来自原点的足够位移高度敏感。
We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chosen fixed point (placed at the origin) with random Gaussian coefficients. The ensuing analysis reveals that as long as the origin remains stable, it is surrounded by a "resilience gap": there are no other fixed points within a radius r*>0 and the system is therefore expected to be resilient to a typical initial displacement small in comparison to r*. The radius r* is shown to vanish at the same threshold where the origin loses local stability, revealing a mechanism by which systems close to the tipping point become less resilient. We also find that beyond the resilience radius the number of fixed points in a ball surrounding the original point of equilibrium grows exponentially with N, making systems dynamics highly sensitive to far enough displacements from the origin.
