Coupled catastrophes: sudden shifts cascade and hop among interdependent systems

Brummitt, Charles D.; Barnett, George A.; D’Souza, Raissa M.

doi:10.1098/rsif.2015.0712

Cited by 72 publications

(99 citation statements)

References 94 publications

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“…Equation 1 is a minimal example for continuous dynamical systems that possess two distinct stable states. Hence, this model can act as a paradigmatic model and has been applied to ecosystems like shallow lakes, but also ice sheets or the thermohaline circulation 6,[34][35][36] . The bifurcation diagram of one of these tipping elements is shown in Fig.…”

Section: A System Of Differential Equationsmentioning

confidence: 99%

How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales

Wunderling

Stumpf

Krönke

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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How motifs condition critical thresholds: Linking Micro-to Macro-scales In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erdős-Rényi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop and the neighboring loop.Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs.We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease of the critical coupling strength.For the highly clustered moisture recycling network in the Amazon, we observe regions of very high motif occurrence for each of the four investigated motifs suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erdős-Rényi network.This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole. a) These authors equally contributed to this study. Correspondences should be addressed to: nico.wunderling@pikpotsdam.de 2 How motifs condition critical thresholds: Linking Micro-to Macro-scales Tipping elements are nonlinear systems, where a small perturbation can be sufficient to induce a qualitative change of the whole system as soon as a critical threshold (tipping point) is crossed. Coupled tipping elements exist for instance in connected lake systems, in the Earth's climate system or in social systems. Here, we investigate networks of interacting tipping elements, where each node consists of a stylized tipping element and explore important interaction structures on the micro scale of the network, the so-called motifs. Such motifs in complex networks have been found in multiple systems such as cell metabolism, food webs or neural networks and are known to be significantly overexpressed in real-world compared to random networks. However, motifs have not yet been studied extensively in complex networks, where nodes have their own dynamics. In our study, we find that tipping cascades occur more often at locations with high motif frequency revealing locations (nodes) of decreased robustness.

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Section: A System Of Differential Equationsmentioning

confidence: 99%

How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales

Wunderling

Stumpf

Krönke

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…In all such cases, an otherwise small perturbation may propagate and eventually cause a sizable portion of the system to fail. Various system-independent cascade models have been proposed [8][9][10][11][12][13] and used to draw general conclusions, such as on the impact of interdependencies [14] and countermeasures [15]. There are outstanding questions, however, for which it is necessary to model the cascade dynamics starting from the actual dynamical state of the system.…”

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confidence: 99%

Cascading Failures as Continuous Phase-Space Transitions

Yang¹,

Motter²

2017

Phys. Rev. Lett.

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In network systems, a local perturbation can amplify as it propagates, potentially leading to a largescale cascading failure. Here we derive a continuous model to advance our understanding of cascading failures in power-grid networks. The model accounts for both the failure of transmission lines and the desynchronization of power generators, and incorporates the transient dynamics between successive steps of the cascade. In this framework, we show that a cascade event is a phase-space transition from an equilibrium state with high energy to an equilibrium state with lower energy, which can be suitably described in closed form using a global Hamiltonian-like function. From this function we show that a perturbed system cannot always reach the equilibrium state predicted by quasi-steadystate cascade models, which would correspond to a reduced number of failures, and may instead undergo a larger cascade. We also show that in the presence of two or more perturbations, the outcome depends strongly on the order and timing of the individual perturbations. These results offer new insights into the current understanding of cascading dynamics, with potential implications for control interventions.Cascading processes underlie a myriad of network phenomena [1], including blackouts in power systems [2,3], secondary extinctions in ecosystems [4,5], and complex contagion in financial networks [6,7]. In all such cases, an otherwise small perturbation may propagate and eventually cause a sizable portion of the system to fail. Various system-independent cascade models have been proposed [8][9][10][11][12][13] and used to draw general conclusions, such as on the impact of interdependencies [14] and countermeasures [15]. There are outstanding questions, however, for which it is necessary to model the cascade dynamics starting from the actual dynamical state of the system.In power-grid networks, the state of the system is determined by the power flow over transmission lines and the frequency of the power generators, which must be respectively below capacity and synchronized under normal steady-state conditions. Although a local perturbation has a limited impact on the connectivity of the network, it may trigger a cascade of failures and protective responses that switch off grid components and may also lead generators to lose synchrony. Much of our current understanding about this process has been derived from quasi-steady-state cascade models [16][17][18][19][20][21], which use iterative procedures to model the successive inactivation of network components caused by power flow redistributions, while omitting the transient dynamics between steady states as well as the dynamics of the generators. Further understanding has resulted from stability studies focused on the synchronization dynamics of power generators in the absence of flow redistributions [22][23][24][25][26].Yet, to date no theoretical approach has been developed to incorporate at the same time these two fundamental aspects of power-grid dynamics-frequency change and flow ...

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“…It needs to be stressed that bifurcational tipping, even though often mentioned, is not the only possible type of tipping [23,44,48,50]. Nevertheless, the response of many natural systems to a control parameter can be described in terms of a double fold bifurcation [47,51,52]. Real-world tipping elements are not independent from each other [51] but there may exist complex interactions between them.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, the response of many natural systems to a control parameter can be described in terms of a double fold bifurcation [47,51,52]. Real-world tipping elements are not independent from each other [51] but there may exist complex interactions between them. Potential interactions through various physical mechanisms were revealed for tipping elements in the climate system [53].…”

Section: Introductionmentioning

confidence: 99%

Dynamic emergence of domino effects in systems of interacting tipping elements in ecology and climate

Klose¹,

Karle²,

Winkelmann³

et al. 2020

Preprint

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In ecology, climate and other fields, systems have been identified that can transition into a qualitatively different state when a critical threshold or tipping point in a driving process is crossed. An understanding of those tipping elements is of great interest given the increasing influence of humans on the biophysical Earth system. Tipping elements are not independent from each other as there exist complex interactions, e.g. through physical mechanisms that connect subsystems of the climate system. Based on earlier work on such coupled nonlinear systems, we systematically assessed the qualitative asymptotic behavior of interacting tipping elements. We developed an understanding of the consequences of interactions on the tipping behavior allowing for domino effects and tipping cascades to emerge under certain conditions. The application of these qualitative results to real-world examples of interacting tipping elements shows that domino effects with profound consequences can occur: the interacting Greenland ice sheet and thermohaline ocean circulation might tip before the tipping points of the isolated subsystems are crossed. The eutrophication of the first lake in a lake chain might propagate through the following lakes without a crossing of their individual critical nutrient input levels. The possibility of emerging domino effects calls for the development of a unified theory of interacting tipping elements and the quantitative analysis of interacting real-world tipping elements.

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Coupled catastrophes: sudden shifts cascade and hop among interdependent systems

Cited by 72 publications

References 94 publications

How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales

How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales

Cascading Failures as Continuous Phase-Space Transitions

Dynamic emergence of domino effects in systems of interacting tipping elements in ecology and climate

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