Microtransition cascades to percolation.
We report the discovery of a discrete hierarchy of microtransitions occurring in models of continuous and discontinuous percolation. The precursory microtransitions allow us to target almost deterministically the location of the transition point to global connectivity. This extends to the class of intrinsically stochastic processes the possibility to use warning signals anticipating phase transitions in complex systems.
Institute of Computing Technology, Chinese Academy of Sciences, 6 Kexueyuan South Road, Haidian, Beijing 100190, China.
Wei
W
Chen
Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Fassberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Faculty of Physics, University of Göttingen, Am Fassberg 17, 37077 Göttingen, Germany.
Malte
M
Schröder
University of California, Davis, California 95616, USA and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
Raissa M
RM
D'Souza
Department of Management, Technology and Economics (D-MTEC), ETH Zurich, Scheuchzerstrasse 7, CH-8092 Zurich, Switzerland.
Didier
D
Sornette
Max Planck Institute for Dynamics and Self-Organization (MPI DS), Am Fassberg 17, 37077 Göttingen, Germany and Institute for Nonlinear Dynamics, Faculty of Physics, University of Göttingen, Am Fassberg 17, 37077 Göttingen, Germany and Department of Management, Technology and Economics (D-MTEC), ETH Zurich, Scheuchzerstrasse 7, CH-8092 Zurich, Switzerland.
Jan
J
Nagler