Document Type : Original Article
Authors
1 Department of physics, University of Qom, Ghom.
2 Department of physics, University of Qom, Ghom
Abstract
We consider two nonlinear electrical circuits consisting of two nonlinear capacitors that are coupled to each other through linear inductors (mutual induction) under the influence of time-dependent external fields. By excitation of two non-linear chaos electrical circuits (chaos oscillators) by each other, the Lyapunov indexes were extracted numerically and the synchronization of two electrical circuits without chaos connection was observed. The dependence of the Lyapunov exponent on the numerical value of the coupling coefficient (mutual induction m) has been studied and the critical value of this coefficient has been determined. Also, the effect of this coupling coefficient of two nonlinear electrical circuits (two Duffing oscillators) coupled without connection has been investigated in order to observe different dynamic states. Diagrams of charge and current changes in terms of time for the numerical value of critical mutual induction have been studied and the synchronization of the two circuits is shown.
Keywords
Main Subjects
- P L Kapitza, Physics 231 (1984)
- C G Steyn and J D Van Wyk, IEEE Trans. Indust. Appl. 3 (1986) 471.
- G Fregien and J D van Wyk, IEEE Trans. Power Electron. 7, 2 (1992) 425.
- C G Steyn and J D Van Wyk, Etz-Archiv 9, 2 (1987) 39.
- E Gluskin, J. Electron. 58, 1 (1985) 63.
- J C Burfoot and G W Taylor, “Polar Dielectrics And Their Applications”, Univ of California Press (2022).
- E Gluskin, de Phys. I 4, 5 (1994) 801.
- A Zamani and H Pahlavani, International Journal of Modern Physics B 36, 02 (2022) 2250014.
- S H Strogatz, “Nonlinear dynamics and chaos: with applications to physics, biology, chemistry and engineering”, Addison-Wesley (1994).
- G Benettin, et al., Theory. Meccanica, 15, 1 (1980) 9.
- H Pahlavani and E R Kolur, B Condens. Matter 495 (2016) 123.
- X Liu and S Y Hui, IEEE Trans. Power Electron.23, 1 (2008), 455.
- M F Mahmood, et al., Designs 5, 4 (2021) 59.
- B Choi, et al.,IEEE Trans. Indust. Electron.51, 1 (2004), 140.
- V B Gore and D H Gawali, 2016 Conference on Advances in Signal Processing (CASP), IEEE (2016).
- S Y R Hui, W Zhong, and C K Lee, IEEE Trans. Power Electron. 29, 9 (2013) 4500.
- A Triviño-Cabrera, Z Lin, and J A Aguado, Energies 11, 3 (2018) 538.
- E Gluskin, Frank. Inst. 336, 7 (1999) 1035.
- P Caldirola, Il Nuovo Cimento (1924-1942), 18, 9 (1941) 393.
- E Kanai, Theor. Phys.3, 4 (1984) 440.
- F L Dubeibe, Colomb. de Fısica 45, 1 (2013).
- M D Hartl, arXiv preprint physics/0303077 (2003).
- M D Hartl, “Dynamics of spinning compact binaries in general relativity”, California Institute of Technology (2003).
- M Sandri, The Mathematica J. (1996) 78.
- B Koocheck Shooshtari, A M Forouzanfar, and M R Molaei. SpringerPlus 5 (2016) 1.
- M Gautherie, et al., Clin. Biol. Res. 107(1982) 279.
- I Kovacic and M J Brennan, “The Duffing equation: nonlinear oscillators and their behaviour”, John Wiley & Sons (2011).
- A Abooee, H A Yaghini-Bonabi, and M R Jahed-Motlagh, Nonlinear Sci. Numer. Simul. 18, 5 (2013) 1235.
- V S Afraimovich, N N Verichev, and M I Rabinovich, Quant. Electron. 29, 9 (1986) 795.
- N F Rulkov, et al., Rev. E 51, 2 (1995) 980.
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