Abstract
Recently it has been shown that building networks from time series allows to study complex systems to characterize them when they go through a phase transition. This give us the opportunity to study this systems from a entire new point of view. In the present work we have used the natural and horizontal visualization algorithms to built networks of two popular models, which present phase transitions: the Ising model and the Kuramoto model. By measuring some topological quantities as the average degree, or the clustering coefficient, it was found that the networks retain the capability of detecting the phase transition of the system. From our results it is possible to establish that both visibility algorithms are capable of detecting the critical control parameter, as in every quantity analyzed (the average degree, the average path and the clustering coefficient) there is a minimum or a maximum value. In the case of the natural visualization algorithm, the average path results are much more noisy than in the other quantities in the study. Specially for the Kuramoto Model, which in this case does not allow a detection of the critical point at plain sight as for the other quantities. The horizontal visualization algorithm has proven to be more explicit in every quantity, as every one of them show a clear change of behavior before and after the critical point of the transition.
Highlights
One of the most important properties that is common to all complex systems is the presence of critical thresholds in their dynamics [1] at which the systems shift abruptly from one state to another
In the present work we have constructed networks from series of two different models: the Ising and the Kuramoto model, these where selected for their importance and the properties they have in what refers to phase transitions
Because the networks inherit some of the properties of the time series (TS), we have analyzed some topological quantities of the networks to verify if they serve as early warning (EW), knowing that the TS analysis are capable of detecting if the system is about to undergo a transition phase
Summary
One of the most important properties that is common to all complex systems is the presence of critical thresholds in their dynamics [1] at which the systems shift abruptly from one state to another. There is a growing interest to understand how a complex system behaves near catastrophic shifts to predict and eventually to control the timing and evolution of such transitions [2,3,4,5,6]. The search for indicators that can predict these shifts has been quite fruitful, with the discovery of the so-called early warning (EW) signals [1]. Ising and Kuramoto models analyzed through visualization algorithms
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