ArticleScientific reports2017
How to test for partially predictable chaos.
Article in Scientific reports, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks.Entropy (Basel, Switzerland) · 2021Article
- Chaos theory discloses triggers and drivers of plankton dynamics in stable environment.Scientific reports · 2019Article
- Article
- E-I balance emerges naturally from continuous Hebbian learning in autonomous neural networks.Scientific reports · 2018Article
- Closed-loop Robots Driven by Short-Term Synaptic Plasticity: Emergent Explorative vs. Limit-Cycle Locomotion.Frontiers in neurorobotics · 2016Article
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Authors and funding
3 authors.
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Abstract
For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.
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Registered trials
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