Detection of quasi-periodic processes in complex systems: How do we quantitatively describe their properties?

Physica Scripta

Volumn 89, Issue 1, 2014, Pages

  Nigmatullin, Raoul R ^a   Khamzin, Airat A ^a   Tenreiro Machado, J ^b  

^a KAZAN FEDERAL UNIVERSITY   (Russian Federation)

^b INSTITUTO SUPERIOR DE ENGENHARIA DO PORTO   (Portugal)

Author keywords

complex systems; quasi periodic process; random data processing; the generalized Prony spectrum

Indexed keywords

AMPLITUDE FREQUENCY RESPONSE; DETECTION ALGORITHM; FOURIER SPECTROSCOPY; QUANTITATIVE PARAMETERS; QUASI-PERIODIC PROCESS; SPATIAL STRUCTURE; SPECTROSCOPIC DATA; THE GENERALIZED PRONY SPECTRUM;

DATA PROCESSING; LARGE SCALE SYSTEMS;

FREQUENCY RESPONSE;

EID: 84891868377     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/89/01/015201     Document Type: Article

References (17)

1. Mandelbrot B 1982 Fractal Geometry of Nature San Francisco, CA: Freeman
2. Aharony A and Feder J (ed) 1989 Fractals in physics Essays in Honour of B Mandelbrot (North-Holland: Amsterdam)
3. Samko S G, Kilbas A A and Marichev O I 1987 Integrals and Derivatives of the Fractional Order and their Some Applications (Minsk: Nauka and Tekhnika' Publishing House) p 688 (in Russian)
4. Machado J A T, Kiryakova V and Mainardi F 2011 Recent history of fractional calculus Commun. Nonlinear Sci. Numer. Simul. 16 1140
5. Nigmatullin R R, Machado J A and Tand Menezes R 2013 Self-similarity principle: the reduced description of randomness Central Eur. J. Phys. 11 724-39
6. Nigmatullin R R 2012 J. Appl. Nonlinear Dyn. 1 207
7. Kwapien J and Drozdz S 2012 Phys. Rep. 515 115
8. Nigmatullin R R 2008 Phys. Wave Phenom. 16 119
9. Osborne M R and Smyth G K 1991 A modified Prony algorithm for fitting functions defined by difference equations SIAM J. Sci. Stat. Comput. 12 362
10. Kahn M, Mackisack M S, Osborne M R and Smyth G K 1992 On the consistency of Prony's method and related algorithms J. Comput. Graph. Stat. 1 329
11. Osborne M R and Smyth G K 1995 A modified Prony algorithm for fitting sums of exponential functions SIAM J. Sci. Stat. Comput. 16 119
12. Nigmatullin R R 2006 The statistics of the fractional moments: is there any chance to read 'quantitatively'any randomness? J. Signal Process. 86 2529 (Pubitemid 44026628)
13. Nigmatullin R R 2010 Universal distribution function for the strongly-correlated fluctuations: general way for description of random sequences Commun. Nonlinear Sci. Numer. Simul. 15 637
14. Nigmatullin R R, Ionescu C and Baleanu D 2013 NIMRAD: novel technique for respiratory data treatment J. Signal Video Process. doi:10.1007/s11760-012- 0386-1
15. Ciurea M L, Lozanu S, Stavaracher I, Lepadatu A M, Iancu V, Mitroi M R, Nigmatullin R and Baleanu C M 2011 Stressed induced traps in multilayed structures J. Appl. Phys. 109 013717
16. Pershin S M, Bunkin A F, Lukyanchenko V A and Nigmatullin R R 2007 Detection of the OH band fine structure in a liquid water by means of new treatment procedure based on the statistics of the fractional moments Lazer Phys. Lett. 4 809
17. Pershin S M, Bunkin A F and Lukyanchenko V A 2010 Evolution of the spectral components of ice in the OH band of water at temperatures 13-99 C Quantum Electron. 40 1146