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.
Subject(s)
Models, Biological , Biological Evolution , Communicable Diseases/epidemiology , Disease Outbreaks/statistics & numerical data , Disease Susceptibility/epidemiology , Epidemics/statistics & numerical data , Game Theory , Humans , Measles/epidemiology , United Kingdom/epidemiologyABSTRACT
SUMMARY: The largenet2 C++ library provides an infrastructure for the simulation of large dynamic and adaptive networks with discrete node and link states. AVAILABILITY: The library is released as free software. It is available at http://biond.github.com/largenet2. Largenet2 is licensed under the Creative Commons Attribution-NonCommercial 3.0 Unported License. CONTACT: gerd@biond.org
Subject(s)
Computer Simulation , Software , Epidemiologic StudiesABSTRACT
We consider voter dynamics on a directed adaptive network with fixed out-degree distribution. A transition between an active phase and a fragmented phase is observed. This transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out-degree distribution. However, if a significant number of nodes with low out degree is present, then fragmentation can occur even far below the estimated critical point due to the formation of self-stabilizing structures that nucleate fragmentation. This process may be relevant for fragmentation in current political opinion formation processes.