Early warning signs for saddle-escape transitions in complex networks.
Bottom Line:
We illustrate our results in two network models and epidemiological data.This work thus establishes a connection from critical transitions to networks and an early warning sign for a new type of critical transition.In complex models and big data we anticipate that saddle-transitions will be encountered frequently in the future.
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PubMed Central - PubMed
Affiliation: Vienna University of Technology, 1040 Vienna, Austria.
ABSTRACT
Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress builds on a mathematical framework in which a real-world system is described by a low-dimensional equation system with a small number of key variables, where the critical transition often corresponds to a bifurcation. Here we show that in high-dimensional systems, containing many variables, we frequently encounter an additional non-bifurcative saddle-type mechanism leading to critical transitions. This generic class of transitions has been missed in the search for early-warnings up to now. In fact, the saddle-type mechanism also applies to low-dimensional systems with saddle-dynamics. Near a saddle a system moves slowly and the state may be perceived as stable over substantial time periods. We develop an early warning sign for the saddle-type transition. We illustrate our results in two network models and epidemiological data. This work thus establishes a connection from critical transitions to networks and an early warning sign for a new type of critical transition. In complex models and big data we anticipate that saddle-transitions will be encountered frequently in the future. No MeSH data available. |
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Mentions: Increasing p at a constant rate from a small initial value, we observe two main dynamical changes. First, a stationary solution turns into stable oscillations, which increase in amplitude and period. Here we observe the classical increase in variance before a Hopf bifurcation111 (Fig. 2(b1)), which is a good predictor for the transition from random fluctuations to small deterministic oscillations. Second, critical transitions occur at larger rewiring rates, where the cooperator density x1(t) drops sharply to lower values before rising again slowly. These transitions are associated to the presence of a homoclinic loop in the system22, which is attached to the fully cooperative state . |
View Article: PubMed Central - PubMed
Affiliation: Vienna University of Technology, 1040 Vienna, Austria.
No MeSH data available.