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Crash of seemingly stable social systems: new dynamics detected

09/30/2016 - From Facebook to international climate agreements like the Paris accord that is currently in the ratification process, the stability of complex social networks is still poorly understood. To better assess system crash likelihood, an international team of scientists now proposes a new mathematical system dynamics model. One key factor for system collapse is individual action based on local information, the study finds. When a member of the network - be it a person or a state - observes friends or allies to leave the system, it likely opts out as well. Small perturbations can hence have huge impacts.
Crash of seemingly stable social systems: new dynamics detected

Because node 1 has lost more than 50% of its original neighbors, it will leave in the next time step, which leaves each of the three nodes within the blue triangle with fewer than three connections, leading to network crash. Fig 1 from Yu et al, 2016

“While some weakened systems survive for a surprisingly long time, others that seem too big to fail suddenly crash,” says Jürgen Kurths from the Potsdam Institute for Climate Impact Research, team lead for the study to be published next week in the Proceedings of the US National Academy of Sciences (PNAS). So far, cascade models could not properly explain this since they’re focused on the sheer number of connections in a network – our new approach adds to that by analyzing the structure of the connections and by integrating the dynamics of change, or some memory-like behavior of the participants. “If you’re in a social network, you compare how many friends you have today and how many you had maybe a year ago – if the loss rate is high, you decide to leave” explains Kurths. “Since many members of the network act this way, it is doomed to die.

However, this of course depends on the surrounding conditions. For instance, the likelihood of leaving a system is higher when there’s an attractive alternative to go to. Also, each system has specific characteristics determining the change process which are sometimes hard to identify.

Still, the new approach can principally be applied to any complex network. Data from the failed social network Friendster has been used by the scientists to successfully test their model – the network had more than 60 million members in 2008 before rapidly loosing users and eventually ending. The scientist think that their new approach of analyzing network dynamics might be applied to the adoption process of new technologies such as rooftop solar panels, the sudden termination of the Qing Dynasty  in China a century ago, and even to natural systems such as understanding of formation and destruction of animal herds or amphibian populations.

Article: Yi Yu, Gaoxi Xiao, Jie Zhou, Yubo Wang, Zhen Wang, Jürgen Kurths, Hans Joachim Schellnhuber (2016): System crash as dynamics of complex networks. Proceedings of the US National Academy of Sciences (PNAS, Early Edition) [DOI:10.1073/pnas.1612094113]

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