The human brain1, 2, power grids3, arrays of coupled lasers4 and the Amazon rainforest5, 6 are all characterized by multistability7. 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 topologies8, 9, 10 of neural networks and power grids, which have eluded theoretical description based solely on linear stability11, 12, 13. We anticipate that basin stability will provide a powerful tool for complex systems studies, including the assessment of multistable climatic tipping elements14.
- statistical physics
- thermodynamics and nonlinear dynamics