Network risk and forecasting power in phase-flipping dynamical networks.
To model volatile real-world network behavior, we analyze a phase-flipping dynamical scale-free network in which nodes and links fail and recover. We investigate how stochasticity in a parameter governing the recovery process affects phase-flipping dynamics, and we find the probability that no more than q% of nodes and links fail. We derive higher moments of the fractions of active nodes and active links, fn(t) and fℓ(t), and we define two estimators to quantify the level of risk in a network. We find hysteresis in the correlations of fn(t) due to failures at the node level, and we derive conditional probabilities for phase-flipping in networks. We apply our model to economic and traffic networks.
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA and Faculty of Civil Engineering, University of Rijeka, 51000 Rijeka, Croatia and Zagreb School of Economics and Management, 10000 Zagreb, Croatia and Faculty of Economics, University of Ljubljana, 1000 Ljubljana, Slovenia.
B
B
Podobnik
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
A
A
Majdandzic
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
C
C
Curme
NUS Graduate School for Integrative Sciences and Engineering, NUS, Singapore 117456, Singapore and Department of Physics and Center for Computational Science and Engineering, NUS, Singapore 117546, Singapore.
Z
Z
Qiao
School of Business, School of Science, and Research Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China.
W-X
WX
Zhou
Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
H E
HE
Stanley
NUS Graduate School for Integrative Sciences and Engineering, NUS, Singapore 117456, Singapore and Department of Physics and Center for Computational Science and Engineering, NUS, Singapore 117546, Singapore and Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, People's Republic of China.
B
B
Li