松散模型分析无需正规形分析即可识别分岔参数
Sloppy model analysis identifies bifurcation parameters without Normal Form analysis
AI总结：
本文提出时间拓宽信息几何方法，利用松散模型分析直接处理分岔以快速刻画系统拓扑非均匀性，无需正规形分析。
摘要：
分岔现象在多维多参数动力系统中普遍存在。正规形理论表明，分岔本身由相对较少的参数驱动；然而，这些参数通常是方程所表达的原始参数的非线性组合。发现能够将此类复杂原始方程变换为正规形的重参数化往往非常困难，而且该重参数化甚至可能不存在闭式形式。近期进展已将信息几何和分岔与重整化群联系起来。在此，我们证明松散模型分析（一种信息几何方法）可直接用于时间尺度递增的分岔，从而快速刻画系统的拓扑非均匀性，无论系统是否处于正规形。我们预期这种新颖的分析方法——我们称之为时间拓宽信息几何（TWIG）——将在应用网络分析中发挥作用。
英文摘要：
Bifurcation phenomena are common in multi-dimensional multi-parameter dynamical systems. Normal form theory suggests that the bifurcations themselves are driven by relatively few parameters; however, these are often nonlinear combinations of the bare parameters in which the equations are expressed. Discovering reparameterizations to transform such complex original equations into normal-form is often very difficult, and the reparameterization may not even exist in a closed-form. Recent advancements have tied both information geometry and bifurcations to the Renormalization Group. Here, we show that sloppy model analysis (a method of information geometry) can be used directly on bifurcations of increasing time scales to rapidly characterize the system's topological inhomogeneities, whether the system is in normal form or not. We anticipate that this novel analytical method, which we call time-widening information geometry (TWIG), will be useful in applied network analysis.
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