permaculture

[Lawrence London <lfljvenaura@gmail.com>]

(may be of interest to many)

Universal resilience patterns in complex networks : Nature : Nature
Publishing Group
http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html

Universal resilience patterns in complex networks

   - Jianxi Gao
   
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#auth-1>
   ,
   - Baruch Barzel
   
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#auth-2>
   - & Albert-László Barabási
   
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#auth-3>


   - Affiliations
   
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#affil-auth>
   - Contributions
   
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#contrib-auth>
   - Corresponding author
   
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#corres-auth>

Nature 530,307–312(18 February 2016)doi:10.1038/nature16948 Received 13
July 2015 Accepted 14 December 2015 Published online 17 February 2016
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Resilience, a system’s ability to adjust its activity to retain its basic
functionality when errors, failures and environmental changes occur, is a
defining property of many complex systems1
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#ref1>.
Despite widespread consequences for human health2
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#ref2>,
the economy3
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#ref3>
and the environment4
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#ref4>,
events leading to loss of resilience—from cascading failures in
technological systems5
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#ref5>
to mass extinctions in ecological networks6
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#ref6>—are
rarely predictable and are often irreversible. These limitations are rooted
in a theoretical gap: the current analytical framework of resilience is
designed to treat low-dimensional models with a few interacting components7
<http://www.nature.com/nature/journal/v530/n7590/full/nature16948.html#ref7>,
and is unsuitable for multi-dimensional systems consisting of a large
number of components that interact through a complex network. Here we
bridge this theoretical gap by developing a set of analytical tools with
which to identify the natural control and state parameters of a
multi-dimensional complex system, helping us derive effective
one-dimensional dynamics that accurately predict the system’s resilience.
The proposed analytical framework allows us systematically to separate the
roles of the system’s dynamics and topology, collapsing the behaviour of
different networks onto a single universal resilience function. The
analytical results unveil the network characteristics that can enhance or
diminish resilience, offering ways to prevent the collapse of ecological,
biological or economic systems, and guiding the design of technological
systems resilient to both internal failures and environmental changes.
Subject terms:

   - Phase transitions and critical phenomena
   <http://www.nature.com/nature/archive/subject.html?code=2795>
   - Nonlinear phenomena
   <http://www.nature.com/nature/archive/subject.html?code=2803>
   - Civil engineering
   <http://www.nature.com/nature/archive/subject.html?code=986>
   - Complex networks
   <http://www.nature.com/nature/archive/subject.html?code=2801>