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JOURNALS // Vestnik KRAUNC. Fiziko-Matematicheskie Nauki

Vestnik KRAUNC. Fiz.-Mat. Nauki, 2022, Volume 41, Number 4, Pages 146–166 (Mi vkam576)

Investigation of the Selkov fractional dynamical system
R. I. Parovik

References

1. Kearey Ph., The Encyclopedia of Solid Earth Sciences, Blackwell Sci., 1993, 722 pp.
2. Makovetskii V. I., Dudchenko I. P., Zakupin A. S., “Avtokolebatelnaya model istochnikov mikroseism”, Geosistemy perekhodnykh zon, 2017, no. 4(1), 37-46
3. Shpielberg O., Akkermans E. Le, “Chatelier principle for out-of-equilibrium and boundary-driven systems: Application to dynamical phase transitions”, Physical review letters, 116:24 (2016), 240603  crossref  elib
4. Selkov E. E., “Self-oscillations in glycolysis. I. A simple kinetic model”, Eur. J. Biochem., 4 (1968), 79–86  crossref
5. Rabotnov Yu. N., Elementy nasledstvennoi mekhaniki tverdogo tela, Mir, M., 1980, 392 pp.
6. Volterra V., “Sur les' equations int'egro-differentielles et leurs applications”, Acta Mathematica, 35:1 (1912), 295–356  crossref
7. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006, 523 pp.
8. Oldham K. B., Spanier J., The fractional calculus. Theory and applications of differentiation and integration to arbitrary order, Academic Press, London, 1974, 240 pp.
9. Miller K. S., Ross B., An introduction to the fractional calculus and fractional differntial equations, A Wiley-Interscience publication, New York, 1993, 384 pp.
10. Petras I., Fractional Order Nonlinear Systems. Modeling, Analysis and Simulation, Springer, Beijing-Springer-Verlag Berlin Heidelberg, 2011.
11. Brechmann P., Rendall A. D., “Dynamics of the Selkov oscillator”, Mathematical Biosciences, 306 (2018), 152-159 DOI: 10.1016/j.mbs.2018.09.012.  crossref
12. Patnaik S., Hollkamp J. P., Semperlotti F., “Applications of variable-order fractional operators: A review”, Proc. R. Soc. A R. Soc. Publ., 476 (2020), 20190498 DOI: 10.1098/rspa.2019.0498.  crossref
13. Garrappa R., “Numerical Solution of Fractional Differential Equations: A Survey and a Software Tutorial”, Mathematics, 6:16 DOI:10.3390/math6020016. (2018)
14. Yang C., Liu F., “A computationally effective predictor-corrector method for simulating fractional-order dynamical control system”, ANZIAM J., 47 (2006), 168–184 DOI: 10.21914/anziamj.v47i0.1037  crossref
15. Diethelm K, Ford N.J., Freed A.D., “A predictor-corrector approach for the numerical solution of fractional differential equations”, Nonlinear Dyn., 29 (2002), 3-22 DOI: 10.1023/A:1016592219341  crossref
16. Parovik R., Rakhmonov Z., Zunnunov R., “Modeling of fracture concentration by Sel’kov fractional dynamic system”, E3S Web of Conferences, 196 (2020), 02018  crossref
17. Parovik R. I., “Research of the stability of some hereditary dynamic systems”, Journal of Physics: Conference Series, 1141:1 (2018), 012079  crossref
18. Parovik R. I., “Chaotic modes of a non-linear fractional oscillator”, IOP Conference Series: Materials Science and Engineering, 919:5 (2020), 052040  crossref
19. Parovik R. I., “Quality factor of forced oscillations of a linear fractional oscillator”, Technical Physics, 65:7 (2020), 1015-1019  crossref
20. Benettin G., Galgani L., Giorgilli A., Strelcyn J. M., “Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems; a method for computing all of them. Part 1: Theory”, Meccanica, 15:1 (1980), 9-20  crossref
21. Wolf A., Swift, J. B., Swinney, H. L., Vastano, J. A., “Determining Lyapunov exponents from a time series”, Physica D: nonlinear phenomena, 16:3 (1985), 285-317  crossref
22. Ma S., Xu Y., Yue W., “Numerical solutions of a variable-order fractional financial system”, Journal of Applied Mathematics. 2012 (2012), 417942 DOI: 10.1155/2012/417942.
23. Geist K., Parlitz U., Lauterborn W., “Comparision of different methods for computing Lyapunov exponents”, Prog. Theor. Phys., 83:5 (1990)  crossref
24. Parovik R. I., “Studies of the Fractional Selkov Dynamical System for Describing the Self-Oscillatory Regime of Microseisms”, Mathematics, 10(22) (2022), 4208 DOI: 10.3390/math10224208.  crossref


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