Multiple tipping points and optimal repairing in interacting networks.

Systems composed of many interacting dynamical networks-such as the human body with its biological networks or the global economic network consisting of regional clusters-often exhibit complicated collective dynamics. Three fundamental processes that are typically present are failure, damage spread and recovery. Here we develop a model for such systems and find a very rich phase diagram that becomes increasingly more complex as the number of interacting networks increases. In the simplest example of two interacting networks we find two critical points, four triple points, ten allowed transitions and two 'forbidden' transitions, as well as complex hysteresis loops. Remarkably, we find that triple points play the dominant role in constructing the optimal repairing strategy in damaged interacting systems. To test our model, we analyse an example of real interacting financial networks and find evidence of rapid dynamical transitions between well-defined states, in agreement with the predictions of our model.

Complex patterns in the oil market

El patrón de las series temporales de precios y volúmenes del petroleo crudo Brent vendido en la International Petroleum Exchange (Londres), fue analizado utilizando técnicas de análisis no lineal desarrolladas para sistemas complejos. Los análisis muestran que las variaciones en el índice de precios y volúmenes de petróleo negociados no son aleatorias y difieren entre ellos. Las variaciones en precios son asimétricas respecto al tiempo mostrando mayor probabilidad para descensos grandes en comparación a aumentos de precio. Los valores del índice de precios muestran períodos cortos de tiempo más o menos estables, sugiriendo fuertes restriccionespara cambios de precios pero no para volúmenes