ArticleScientific reports2019
Tipping phenomena in typical dynamical systems subjected to parameter drift.
Article in Scientific reports, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Depletion of microglial compensation in glial network: Disease-associated response dynamics in the revised amyloid hypothesis.Neuroprotection (Chichester, England) · 2026Review
- Generalized paradox of enrichment: noise-driven rare rarity in degraded ecological systems.Journal of the Royal Society, Interface · 2025Article
- Non-linear dynamical approaches for characterizing multi-sector climate impacts under irreducible uncertainty.NPJ climate and atmospheric science · 2025Review
- Time-scale synchronisation of oscillatory responses can lead to non-monotonous R-tipping.Scientific reports · 2023Article
- Heteroclinic networks for brain dynamics.Frontiers in network physiology · 2023Review
- Pattern breaking: a complex systems approach to psychedelic medicine.Neuroscience of consciousness · 2023Article
- Phase tipping: how cyclic ecosystems respond to contemporary climate.Proceedings. Mathematical, physical, and engineering sciences · 2021Article
- Tipping points induced by parameter drift in an excitable ocean model.Scientific reports · 2021Article
- Risk of tipping the overturning circulation due to increasing rates of ice melt.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
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3 authors.
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Abstract
Tipping phenomena, i.e. dramatic changes in the possible long-term performance of deterministic systems subjected to parameter drift, are of current interest but have not yet been explored in cases with chaotic internal dynamics. Based on the example of a paradigmatic low-dimensional dissipative system subjected to different scenarios of parameter drifts of non-negligible rates, we show that a number of novel types of tippings can be observed due to the topological complexity underlying general systems. Tippings from and into several coexisting attractors are possible, and one can find fractality-induced tipping, the consequence of the fractality of the scenario-dependent basins of attractions, as well as tipping into a chaotic attractor. Tipping from or through an extended chaotic attractor might lead to random tipping into coexisting regular attractors, and rate-induced tippings appear not abruptly as phase transitions, rather they show up gradually when the rate of the parameter drift is increased. Since chaotic systems of arbitrary time-dependence call for ensemble methods, we argue for a probabilistic approach and propose the use of tipping probabilities as a measure of tipping. We numerically determine these quantities and their parameter dependence for all tipping forms discussed.
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