ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Guyo G. A., Pavlov A. N. Application of joint singularity spectrum to analyze cooperative dynamics of complex systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2023, vol. 31, iss. 3, pp. 305-315. DOI: 10.18500/0869-6632-003041, EDN: RALPKR

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
57.087
DOI: 
10.18500/0869-6632-003041
EDN: 
RALPKR

Application of joint singularity spectrum to analyze cooperative dynamics of complex systems

Autors: 
Guyo German Aleksandrovich, Saratov State University
Pavlov Aleksej Nikolaevich, Saratov State University
Abstract: 

Purpose of this work is to generalize the wavelet-transform modulus maxima method to the case of cooperative dynamics of interacting systems and to introduce the joint singularity spectrum into consideration.

The research method is the wavelet-based multifractal formalism, the generalized version of which is used to quantitatively describe the effect of chaotic synchronization in the dynamics of model systems. Models of coupled Rossler systems and paired nephrons are considered.

As a result of the studies carried out, the main changes in the joint singularity spectra were noted during the transition from synchronous to asynchronous oscillations in the first model and to the partial synchronization mode in the second model.

Conclusion. Proposed approach can be used in studies of the cooperative dynamics of systems of various nature.

Key words: 
multifractal formalism
joint singularity spectrum
synchronization of oscillations
wavelet transform
Acknowledgments: 
This work was supported by Russian Science Foundation, project No. 22-22-00065
Reference: 
  1. Bendat JS, Piersol AG. Random Data: Analysis and Measurement Procedures. 4th edition. New Jersey: John Wiley & Sons; 2010. 640 p. DOI: 10.1002/9781118032428.
  2. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes: The Art of Scientific Computing. 3rd edition. Cambridge: Cambridge University Press; 2007. 1256 p.
  3. Halsey TC, Jensen MH, Kadanoff LP, Procaccia I, Shraiman BI. Fractal measures and their singularities: The characterization of strange sets. Phys. Rev. A. 1986;33(2):1141–1151. DOI: 10. 1103/PhysRevA.33.1141.
  4. Frish U, Parisi G. On the singularity structure of fully developed turbulence. In: Ghil M, Benzi R, Parisi G, editors. Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics. New York: North-Holland; 1985. P. 84–88.
  5. Benzi R, Vulpiani A. Multifractal approach to fully developed turbulence. Rendiconti Lincei. Scienze Fisiche e Naturali. 2022;33(3):471–477. DOI: 10.1007/s12210-022-01078-5.
  6. Muzy JF, Bacry E, Arneodo A. Wavelets and multifractal formalism for singular signals: Application to turbulence data. Phys. Rev. Lett. 1991;67(25):3515–3518. DOI: 10.1103/ PhysRevLett.67.3515.
  7. Muzy JF, Bacry E, Arneodo A. The multifractal formalism revisited with wavelets. International Journal of Bifurcation and Chaos. 1994;4(2):245–302. DOI: 10.1142/S0218127494000204.
  8. Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Havlin S, Bunde A, Stanley HE. Multifractal detrended fluctuation analysis of nonstationary time series. Physica A: Statistical Mechanics and its Applications. 2002;316(1–4):87–114. DOI: 10.1016/S0378-4371(02)01383-3.
  9. Ihlen EAF. Introduction to multifractal detrended fluctuation analysis in Matlab. Frontiers in Physiology. 2012;3:141. DOI: 10.3389/fphys.2012.00141.
  10. Meneveau C, Sreenivasan KR, Kailasnath P, Fan MS. Joint multifractal measures: Theory and applications to turbulence. Phys. Rev. A. 1990;41(2):894–913. DOI: 10.1103/PhysRevA.41.894.
  11. Ivanov PC, Amaral LAN, Goldberger AL, Havlin S, Rosenblum MG, Struzik ZR, Stanley HE. Multifractality in human heartbeat dynamics. Nature. 1999;399(6735):461–465. DOI: 10.1038/ 20924.
  12. Pavlov AN, Sosnovtseva OV, Ziganshin AR, Holstein-Rathlou NH, Mosekilde E. Multiscality in the dynamics of coupled chaotic systems. Physica A: Statistical Mechanics and its Applications. 2002;316(1–4):233–249. DOI: 10.1016/S0378-4371(02)01202-5.
  13. Pavlov AN, Pavlova ON, Abdurashitov AS, Sindeeva OA, Semyachkina-Glushkovskaya OV, Kurths J. Characterizing scaling properties of complex signals with missed data segments using the multifractal analysis. Chaos. 2018;28(1):013124. DOI: 10.1063/1.5009438.
  14. Addison PS. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and Finance. 2nd edition. Boca Raton: CRC Press; 2016. 464 p. DOI: 10.1201/9781315372556.
  15. Barfred M, Mosekilde E, Holstein-Rathlou NH. Bifurcation analysis of nephron pressure and flow regulation. Chaos. 1996;6(3):280–287. DOI: 10.1063/1.166175.
  16. Postnov DE, Sosnovtseva OV, Mosekilde E, Holstein-Rathlou NH. Cooperative phase dynamics in coupled nephrons. International Journal of Modern Physics B. 2001;15(23):3079–3098. DOI: 10.1142/S0217979201007233.
  17. Sosnovtseva OV, Pavlov AN, Mosekilde E, Yip KP, Holstein-Rathlou NH, Marsh DJ. Synchronization among mechanisms of renal autoregulation is reduced in hypertensive rats. Am. J. Physiol. Renal. Physiol. 2007;293(5):F1545–F1555. DOI: 10.1152/ajprenal.00054.2007.
Received: 
23.01.2023
Accepted: 
04.04.2023
Available online: 
21.04.2023
Published: 
31.05.2023
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