A look into chaos detection through topological data analysis

Physica D: Nonlinear Phenomena - Tập 406 - Trang 132446 - 2020
Joshua R. Tempelman1, Firas A. Khasawneh1
1Dept. of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA

Tài liệu tham khảo

Benettin, 1980, Lyapunov characteristic exponents for smooth dynamical systems and for hamiltonian systems: A method for computing all of them. part 2: Numerical application, Meccanica, 15, 21, 10.1007/BF02128237 Wolf, 1985, Determining Lyapunov exponents from a time series, Physica D, 16, 285, 10.1016/0167-2789(85)90011-9 Wernecke, 2017, How to test for partially predictable chaos, Sci. Rep., 7, 10.1038/s41598-017-01083-x Gottwald, 2004, A new test for chaos in deterministic systems, Proc. R. Soc. A, 460, 603, 10.1098/rspa.2003.1183 Gottwald, 2005, Testing for chaos in deterministic systems with noise, Physica D, 212, 100, 10.1016/j.physd.2005.09.011 Gottwald, 2009, On the implementation of the 0–1 test for chaos, SIAM J. Appl. Dyn. Syst., 8, 129, 10.1137/080718851 Skokos, 2016 Gottwald, 2016, The 0-1 test for chaos: A review, 221 Lorenz, 1963, Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130, 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 Melosik, 2016, On the 0/1 test for chaos in continuous systems, Bull. Pol. Acad. Sci. Tech. Sci., 64, 521 A. Myers, F. Khasawneh, On the Automatic Parameter Selection for Permutation Entropy, arXiv:http://arxiv.org/abs/1905.06443v1. A.D. Myers, F.A. Khasawneh, Delay Parameter Selection in Permutation Entropy Using Topological Data Analysis, arXiv:http://arxiv.org/abs/1905.04329v1. Gottwald, 2009, On the validity of the 0–1 test for chaos, Nonlinearity, 22, 1367, 10.1088/0951-7715/22/6/006 Robinson, 2014 J.A. Perea, Topological Time Series Analysis, arXiv:http://arxiv.org/abs/1812.05143v1. Khasawneh, 2018, Topological data analysis for true step detection in periodic piecewise constant signals, Proc. R. Soc. A, 474, 10.1098/rspa.2018.0027 Gidea, 2018, Topological recognition of critical transitions in time series of cryptocurrencies, SSRN Electron. J., 10.2139/ssrn.3202721 Khasawneh, 2016, Chatter detection in turning using persistent homology, Mech. Syst. Signal Process., 70–71, 527, 10.1016/j.ymssp.2015.09.046 Khasawneh, 2018, Chatter classification in turning using machine learning and topological data analysis, IFAC-PapersOnLine, 51, 195, 10.1016/j.ifacol.2018.07.222 M.C. Yesilli, F.A. Khasawneh, A. Otto, Topological feature vectors for chatter detection in turning processes, arXiv:http://arxiv.org/abs/1905.08671v2. M.C. Yesilli, S. Tymochko, F.A. Khasawneh, E. Munch, Chatter Diagnosis in Milling Using Supervised Learning and Topological Features Vector, arXiv:http://arxiv.org/abs/1910.12359v1. Offroy, 2016, Topological data analysis: A promising big data exploration tool in biology, analytical chemistry and physical chemistry, Anal. Chim. Acta, 910, 1, 10.1016/j.aca.2015.12.037 Li, 2018, The persistent homology mathematical framework provides enhanced genotype-to-phenotype associations for plant morphology, Plant Physiol., 10.1104/pp.18.00104 Mittal, 2017, Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology, Chaos, 27, 10.1063/1.4983840 J.R. Tempelman, F.A. Khasawneh, Chaos Detection with Persistent Homology, Mendeley Data, http://dx.doi.org/10.17632/4kszknf6vj.2. Munkres, 1993 Munch, 2017, A user’s guide to topological data analysis, J. Learn. Anal., 4, 47 Cohen-Steiner, 2006, Stability of persistence diagrams, Discrete Comput. Geom., 37, 103, 10.1007/s00454-006-1276-5 Ghrist, 2014 Edelsbrunner, 2013 Edelsbrunner, 2008 E. Berry, Y.-C. Chen, J. Cisewski-Kehe, B.T. Fasy, Functional Summaries of Persistence Diagrams, arXiv:http://arxiv.org/abs/1804.01618v1. Botev, 2010, Kernel density estimation via diffusion, Ann. Statist., 38, 2916, 10.1214/10-AOS799 Gottwald, 2008, Comment on “reliability of the 0-1 test for chaos”, Phys. Rev. E, 77, 10.1103/PhysRevE.77.028201 Adler, 2019, Modelling persistence diagrams with planar point processes, and revealing topology with bagplots, J. Appl. Comput. Topol., 3, 139, 10.1007/s41468-019-00035-w Adler, 2010, Persistent homology for random fields and complexes, 124, 10.1214/10-IMSCOLL609 Adler, 2014, Crackle: The homology of noise, Discrete Comput. Geom., 52, 680, 10.1007/s00454-014-9621-6 Kahle, 2013, Limit theorems for betti numbers of random simplicial complexes, Homology, Homotopy Appl., 15, 343, 10.4310/HHA.2013.v15.n1.a17 Rössler, 1976, An equation for continuous chaos, Phys. Lett. A, 57, 397, 10.1016/0375-9601(76)90101-8 Letellier, 1995, Unstable periodic orbits and templates of the Rössler system: toward a systematic topological characterization, Chaos, 5, 271, 10.1063/1.166076 May, 2004, Simple mathematical models with very complicated dynamics, 85