A Modified 0-1 Test for Chaos Detection in Oversampled Time Series Observations

The use of binary 0-1 test for chaos detection is limited to detect chaos in oversampled time series observations. In this paper we propose a modified 0-1 test in which, binary 0-1 test is applied to the discrete map of local maxima and minima of the original observable in contrast to the direct observable. The proposed approach successfully detects chaos in oversampled time series data. This is verified by simulating different numerical simulations of Lorenz and Duffing systems. The simulation results show the efficiency and computational gain of the proposed test for chaos detection in the continuous time dynamical systems.

[1]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[2]  P. Jessen,et al.  Quantum signatures of chaos in a kicked top , 2009, Nature.

[3]  Grzegorz Litak,et al.  Detection of the chaotic behaviour of a bouncing ball by the 0–1 test , 2009 .

[4]  Ch. Skokos,et al.  Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits , 2001 .

[5]  Georg A. Gottwald,et al.  On the Implementation of the 0-1 Test for Chaos , 2009, SIAM J. Appl. Dyn. Syst..

[6]  Sawada,et al.  Measurement of the Lyapunov spectrum from a chaotic time series. , 1985, Physical review letters.

[7]  C. Hommes,et al.  Testing for Nonlinear Structure and Chaos in Economic Time Series , 2006 .

[8]  Grzegorz Litak,et al.  Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0–1 test , 2013 .

[9]  Mototsugu Shintani,et al.  Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors , 2001 .

[10]  Grzegorz Litak,et al.  Identification of chaos in a cutting process by the 0–1 test , 2009 .

[11]  Georg A. Gottwald,et al.  On the validity of the 0–1 test for chaos , 2009, 0906.1415.

[12]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[13]  Loukas Zachilas,et al.  Examining the Chaotic Behavior in Dynamical Systems by Means of the 0-1 Test , 2012, J. Appl. Math..

[14]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[15]  H. Abarbanel,et al.  LYAPUNOV EXPONENTS IN CHAOTIC SYSTEMS: THEIR IMPORTANCE AND THEIR EVALUATION USING OBSERVED DATA , 1991 .

[16]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[17]  G. Litak,et al.  Nonlinear dynamics of a regenerative cutting process , 2012, 1201.4923.

[18]  Georg A. Gottwald,et al.  A new test for chaos in deterministic systems , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[19]  Leon Glass,et al.  Introduction to controversial topics in nonlinear science: is the normal heart rate chaotic? , 2009, Chaos.

[20]  Jianbo Gao,et al.  Reliability of the 0-1 test for chaos. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.