Quantifying stability in complex networks: From linear to basin stability

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 in several cases 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.

Student event: Meet the speaker
We invite you to a student-only discussion-round with Prof. Dr. Jürgen Kurths before his Munich Physics Colloquium talk.
Be curious and feel free to ask any question.
Monday, 23 May 2016, 16:00 h
Seminar room PH 3076 (upper floor), Physik-Department der TUM, Garching