5.7 Lorenz Attractor
129
conclude that the system dynamics is fully chaotic. There are also narrow windows
of hyperchaotic dynamics.
A comparison of the results reported in Table 5.14 with the original results exhibit
an excellent coincidence of Benettin method (original results) and the neural network
method (+4.79%). Wolf and Rosenstein methods yielded the underestimated results
of the LLE value. The worst estimation is obtained by Kantz method.
Employing different sampling frequency does not change a picture of Fourier and
wavelet power spectra. This is also validated by Benettin and Rosenstein methods,
which yield the results very close to the original values in spite of the arbitrary choice
of the sampling frequency.
References
1. Astafeva, N.M.: Wavelet-analysis: basic theory and examples of applications. Succ. Phys. Sci.
166(11), 1145–1170 (1996)
2. May, R.: Simple mathematical model with very complicated dynamics. Nature 261, 45–67
(1976)
3. Sprott, J.C.: Elegant Chaos. Algebraically Simple Chaotic Flows. World Scientific, Singapore
(2010)
4. Hénon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 50(1),
69–77 (1976)
5. Sprott, J.C.: Chaos and Time Series Analysis. Oxford University Press, Oxford (2003)
6. Benettin, G., Galgani, L., Strelcyn, J.M.: Kolmogorov entropy and numerical experiments. Phys.
Rev. A 14, 2338–2345 (1976)
7. Baier, G., Klein, M.: Maximum hyperchaos in generalized Henon maps. Phys. Lett. A 151(6–7),
281–284 (1990)
8. Peitgen, H.-O., Jürgens, H., Saupe, D.: The Rössler attractor. In: Chaos and Fractals: New
Frontiers of Science, pp. 636–646. Springer, Berlin (2004)
9. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atm. Sci. 20(2), 130–141 (1963)
129
conclude that the system dynamics is fully chaotic. There are also narrow windows
of hyperchaotic dynamics.
A comparison of the results reported in Table 5.14 with the original results exhibit
an excellent coincidence of Benettin method (original results) and the neural network
method (+4.79%). Wolf and Rosenstein methods yielded the underestimated results
of the LLE value. The worst estimation is obtained by Kantz method.
Employing different sampling frequency does not change a picture of Fourier and
wavelet power spectra. This is also validated by Benettin and Rosenstein methods,
which yield the results very close to the original values in spite of the arbitrary choice
of the sampling frequency.
References
1. Astafeva, N.M.: Wavelet-analysis: basic theory and examples of applications. Succ. Phys. Sci.
166(11), 1145–1170 (1996)
2. May, R.: Simple mathematical model with very complicated dynamics. Nature 261, 45–67
(1976)
3. Sprott, J.C.: Elegant Chaos. Algebraically Simple Chaotic Flows. World Scientific, Singapore
(2010)
4. Hénon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 50(1),
69–77 (1976)
5. Sprott, J.C.: Chaos and Time Series Analysis. Oxford University Press, Oxford (2003)
6. Benettin, G., Galgani, L., Strelcyn, J.M.: Kolmogorov entropy and numerical experiments. Phys.
Rev. A 14, 2338–2345 (1976)
7. Baier, G., Klein, M.: Maximum hyperchaos in generalized Henon maps. Phys. Lett. A 151(6–7),
281–284 (1990)
8. Peitgen, H.-O., Jürgens, H., Saupe, D.: The Rössler attractor. In: Chaos and Fractals: New
Frontiers of Science, pp. 636–646. Springer, Berlin (2004)
9. Lorenz, E.N.: Deterministic nonperiodic flow. J. Atm. Sci. 20(2), 130–141 (1963)