题 目：How Basin Stability Complements the Linear-Stability Paradigm
报告人：Jürgen Kurths 教授（波茨坦大学/洪堡大学，德国）
The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. We anticipate that basin stability will provide a powerful tool for complex systems studies, including the assessment of multistable climatic tipping elements.
Specifically, we employ a novel component-wise version of basin stability, a nonlinear inspection scheme, to investigate how a grid's degree of stability is influenced by certain patterns in the wiring topology. Various statistics from our ensemble simulations all support one main finding: The widespread and cheapest of all connection schemes, namely dead ends and dead trees, strongly diminish stability. For the Northern European power system we demonstrate that the inverse is also true: `Healing' dead ends by addition of transmission lines substantially enhances stability. This indicates a crucial smart-design principle for tomorrow's sustainable power grids: add just a few more lines to avoid dead ends.
P. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Physics 9, 89 (2013)
Kurth教授的研究领域包括complex synchronization phenomena, complex networks, time series analysis and their applications in climatology, sustainability, physiology, systems biology and engineering。共发表文章400余篇，H-index超过50。美国物理学会会士（2000），欧洲科学院院士（2010）。