Function (biology)

Complex system

World Wide Web

Biology

Computer security

Bridge (graph theory)

Set (abstract data type)

Computer science

Complex network

Risk analysis (engineering)

Distributed computing

Business

Evolutionary biology

Computer network

Vulnerability (computing)

Thermodynamics

Physics

Environmental resource management

Internal medicine

Environmental science

Socio-ecological system

Artificial intelligence

Medicine

Programming language

Resilience (materials science)

Resource (disambiguation)

Nature

An analytical framework is proposed for a complex network to accurately predict its dynamic resilience and unveil the network characteristics that can enhance or diminish resilience. Failing nodes in a complex network, for example, stations in a power grid that are are switched off, can lead to a breakdown of the whole system. The ability of the network to adjust so that it still functions despite the errors is called its resilience. Although — at first glance — the points at which different networks lose their resilience seem to have little in common, Jainxi Gao and colleagues show here that, in fact, resilience has underlying universal features. They develop a universal resilience function that depends on a system's dynamics and topology, and show that this analytical framework readily describes ecological networks, power grids, and gene regulatory networks. Their framework may contribute to understanding the vulnerability of many additional natural and man-made systems. 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. Despite widespread consequences for human health2, the economy3 and the environment4, events leading to loss of resilience—from cascading failures in technological systems5 to mass extinctions in ecological networks6—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, 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.

Universal resilience patterns in complex networks