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      Lost generation: Reflections on resilience and flexibility from an energy system architecture perspective

      , , , , ,
      Applied Energy
      Elsevier BV

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          Deterministic Nonperiodic Flow

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            Catastrophic cascade of failures in interdependent networks.

            Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures ('concurrent malfunction') is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.
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              Simple mathematical models with very complicated dynamics.

              First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hiearchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.
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                Author and article information

                Journal
                Applied Energy
                Applied Energy
                Elsevier BV
                03062619
                September 2021
                September 2021
                : 298
                : 117179
                Article
                10.1016/j.apenergy.2021.117179
                fb517655-73a2-48f1-a54c-d03afbd4b828
                © 2021

                https://www.elsevier.com/tdm/userlicense/1.0/

                https://doi.org/10.15223/policy-017

                https://doi.org/10.15223/policy-037

                https://doi.org/10.15223/policy-012

                https://doi.org/10.15223/policy-029

                https://doi.org/10.15223/policy-004

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