Time-Frequency Analysis of Asymmetric Triaxial Galaxy Model Including Effect of Spherical Dark Halo Component
Affiliation(s)
1 Department of Mathematics, Lakshmibai College, University of Delhi, New Delhi, India. 2 Department of Mathematics, Zakir Husain Delhi College, University of Delhi, New Delhi, India.
1 Department of Mathematics, Lakshmibai College, University of Delhi, New Delhi, India. 2 Department of Mathematics, Zakir Husain Delhi College, University of Delhi, New Delhi, India.
ABSTRACT
A method of time-frequency analysis (TFA) based on wavelets is applied to study the phase space structure of three-dimensional asymmetric triaxial galaxy enclosed by spherical dark halo component. The investigation is carried out in the presence and absence of dark halo component. Time-frequency analysis is based on the extraction of instantaneous frequency from the phase of the continuous wavelet transform. This method is comparatively fast and reliable. This method can differentiate periodic from quasi-periodic, chaotic sticky from chaotic non-sticky, ordered from chaotic and also, it can accurately determine the time interval of the resonance trapping and transitions too. Apart from that, the phenomenon of transient chaos can be explained with the help of time-frequency analysis. Comparison with the method of total angular momentum (denoted as Ltot) proposed recently is also presented.
A method of time-frequency analysis (TFA) based on wavelets is applied to study the phase space structure of three-dimensional asymmetric triaxial galaxy enclosed by spherical dark halo component. The investigation is carried out in the presence and absence of dark halo component. Time-frequency analysis is based on the extraction of instantaneous frequency from the phase of the continuous wavelet transform. This method is comparatively fast and reliable. This method can differentiate periodic from quasi-periodic, chaotic sticky from chaotic non-sticky, ordered from chaotic and also, it can accurately determine the time interval of the resonance trapping and transitions too. Apart from that, the phenomenon of transient chaos can be explained with the help of time-frequency analysis. Comparison with the method of total angular momentum (denoted as Ltot) proposed recently is also presented.
KEYWORDS
Time-Frequency Analysis, Triaxial Galactic Potential, Instantaneous Frequency, Total Angular Momentum
Time-Frequency Analysis, Triaxial Galactic Potential, Instantaneous Frequency, Total Angular Momentum
Cite this paper
Gupta, B. and Kumar, V. (2015) Time-Frequency Analysis of Asymmetric Triaxial Galaxy Model Including Effect of Spherical Dark Halo Component. International Journal of Astronomy and Astrophysics, 5, 106-115. doi: 10.4236/ijaa.2015.52014.
Gupta, B. and Kumar, V. (2015) Time-Frequency Analysis of Asymmetric Triaxial Galaxy Model Including Effect of Spherical Dark Halo Component. International Journal of Astronomy and Astrophysics, 5, 106-115. doi: 10.4236/ijaa.2015.52014.
References
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http://dx.doi.org/10.1002/asna.201212110 [2] Smith, R.H. (1991) The Onset of Chaotic Motion in the Restricted Problem of Three Bodies. Ph.D. Thesis, University of Texas at Austin, Austin. [3] Manos, T., Skokos, C.H. and Antonopoulos, C.H. (2008) Probing the Local Dynamics of Periodic Orbits by the Generalized Alignment Index (GALI) Method. International Journal of Bifurcation and Chaos, 22, 1-17.
http://arxiv.org/pdf/1103.0700v3 [4] Caranicolas, N.D. and Zotos, E.E. (2011) Dark Halos Acting as Chaos Controllers in Asymmetric Triaxial Galaxy Models. Research in Astronomy and Astrophysics, 11, 811-823.
http://dx.doi.org/10.1088/1674-4527/11/7/006 [5] Chandre, C., Wiggins, S. and Uzer, T. (2003) Time-Frequency Analysis of Chaotic Systems. Physica D, 181, 171-196. [6] Deplart, N., Escudie, B., Guillemain, P., Kronland Martinet, R., Tchamichian, P. and Torresani, B. (1992) Asymptotic Wavelet and Gabor Analysis, Extraction of Instantaneous Frequency. IEEE Transactions on Information Theory, 38, 644-664. [7] Vela-Arevalo, L.V. (2002) Time-Frequency Analysis Based on Wavelets for Hamiltonian Systems. Ph.D. Dissertation, California Institute of Technology, Pasadena.
http://resolver.caltech.edu/CaltechETD:etd-03302004-115559 [8] Vela-Arevalo, L.V. and Wiggins, S. (2001) Time-Frequency Analysis of Classical Trajectories of Polyatomic Molecules. International Journal of Bifurcation and Chaos, 11, 1359-1380.
http://dx.doi.org/10.1142/S0218127401002766 [9] Todorovska, M. (2001) Estimation of Instantaneous Frequency of Signals Using the Continuous Wavelet Transform. Department of Civil Engineering, University of Southern California, Report CE 01-07, 2001. [10] Vela-Arevalo, L.V. (2004) Time-Frequency Analysis of the Restricted Three-Body Problem: Transport and Resonance Transitions. Classical and Quantum Gravity, 21, S351-S375. [11] Kandrup, H.H., Vass, I.M. and Sideris, I.V. (2003) Transient Chaos and Resonant Phase Mixing in Violent Relaxation. Monthly Notice of the Royal Astronomical Society, 341, 927-936.
http://dx.doi.org/10.1046/j.1365-8711.2003.06466.x [12] http://www-stat.stanford.edu/~wavelab/ [13] The MathWorks, Inc. (2010) Matlab and Statistics Toolbox Release. The MathWorks, Inc., Natick. [14] Mallat, S. (1999) A Wavelet Tour of Signal Processing. Academic Press, San Diego.
[1] Racoveanu, O. (2014) Comparison of Chaos Detection Methods in the Circular Restricted Three-Body Problem. Astronomische Nachrichten, 335, 877-885.
http://dx.doi.org/10.1002/asna.201212110 [2] Smith, R.H. (1991) The Onset of Chaotic Motion in the Restricted Problem of Three Bodies. Ph.D. Thesis, University of Texas at Austin, Austin. [3] Manos, T., Skokos, C.H. and Antonopoulos, C.H. (2008) Probing the Local Dynamics of Periodic Orbits by the Generalized Alignment Index (GALI) Method. International Journal of Bifurcation and Chaos, 22, 1-17.
http://arxiv.org/pdf/1103.0700v3 [4] Caranicolas, N.D. and Zotos, E.E. (2011) Dark Halos Acting as Chaos Controllers in Asymmetric Triaxial Galaxy Models. Research in Astronomy and Astrophysics, 11, 811-823.
http://dx.doi.org/10.1088/1674-4527/11/7/006 [5] Chandre, C., Wiggins, S. and Uzer, T. (2003) Time-Frequency Analysis of Chaotic Systems. Physica D, 181, 171-196. [6] Deplart, N., Escudie, B., Guillemain, P., Kronland Martinet, R., Tchamichian, P. and Torresani, B. (1992) Asymptotic Wavelet and Gabor Analysis, Extraction of Instantaneous Frequency. IEEE Transactions on Information Theory, 38, 644-664. [7] Vela-Arevalo, L.V. (2002) Time-Frequency Analysis Based on Wavelets for Hamiltonian Systems. Ph.D. Dissertation, California Institute of Technology, Pasadena.
http://resolver.caltech.edu/CaltechETD:etd-03302004-115559 [8] Vela-Arevalo, L.V. and Wiggins, S. (2001) Time-Frequency Analysis of Classical Trajectories of Polyatomic Molecules. International Journal of Bifurcation and Chaos, 11, 1359-1380.
http://dx.doi.org/10.1142/S0218127401002766 [9] Todorovska, M. (2001) Estimation of Instantaneous Frequency of Signals Using the Continuous Wavelet Transform. Department of Civil Engineering, University of Southern California, Report CE 01-07, 2001. [10] Vela-Arevalo, L.V. (2004) Time-Frequency Analysis of the Restricted Three-Body Problem: Transport and Resonance Transitions. Classical and Quantum Gravity, 21, S351-S375. [11] Kandrup, H.H., Vass, I.M. and Sideris, I.V. (2003) Transient Chaos and Resonant Phase Mixing in Violent Relaxation. Monthly Notice of the Royal Astronomical Society, 341, 927-936.
http://dx.doi.org/10.1046/j.1365-8711.2003.06466.x [12] http://www-stat.stanford.edu/~wavelab/ [13] The MathWorks, Inc. (2010) Matlab and Statistics Toolbox Release. The MathWorks, Inc., Natick. [14] Mallat, S. (1999) A Wavelet Tour of Signal Processing. Academic Press, San Diego.