Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology

DOI10.1063/1.4983840zbMath1388.37026OpenAlexW2615208302WikidataQ38747957 ScholiaQ38747957MaRDI QIDQ4642602

Khushboo Mittal, Shalabh Gupta

Publication date: 23 May 2018

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4983840

zbMATH Keywords

nonlinear time seriesbifurcations and chaosPoincaré-Bendixson criteria

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Bifurcations of singular points in dynamical systems (37G10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Time series analysis of dynamical systems (37M10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Complex behavior and chaotic systems of ordinary differential equations (34C28) Dynamical aspects of attractors and their bifurcations (37G35)

Related Items (4)

Topological recognition of critical transitions in time series of cryptocurrencies ⋮ Homology of contact 3-CR-submanifolds of an almost 3-contact hypersurface ⋮ Characterizing the complexity of time series networks of dynamical systems: A simplicial approach ⋮ A look into chaos detection through topological data analysis

Uses Software

• javaPlex
• K2

Cites Work

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• Statistical mechanics of complex systems for pattern identification
• Measuring the strangeness of strange attractors
• Computing persistent homology
• Topological persistence and simplification
• Exploring the topology of dynamical reconstructions
• javaPlex: A Research Software Package for Persistent (Co)Homology
• Ideal spatial adaptation by wavelet shrinkage
• De-noising by soft-thresholding
• Persistent topological features of dynamical systems
• Barcodes: The persistent topology of data

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