Fractal Parametric Oscillator as a Model of a Nonlinear Oscillation System in Natural Mediums

Abstract

The paper presents a model of fractal parametric oscillator. Showing that the solution of such a model exists and is unique. A study of the solution with the aid of diagrams Stratton-Ince. The regions of instability, which can occur parametric resonance. It is suggested that this solution can be any signal, including acoustic.

Share and Cite:

R. Parovik, "Fractal Parametric Oscillator as a Model of a Nonlinear Oscillation System in Natural Mediums," International Journal of Communications, Network and System Sciences, Vol. 6 No. 3, 2013, pp. 134-138. doi: 10.4236/ijcns.2013.63016.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. M. Nakhushev, “Fractional Calculus and Its Application,” Fizmatlit, Moscow, 2003, p. 272.
[2] V. A. Gordeenko, “Vector-Phase Methods in Acoustics,” Fizmatlit, Moscow, 2007, p. 480.
[3] V. A. Nakhusheva, “Differential Equations of Mathematical Models of Non-Local Processes,” Nauka, Moscow, 2006, p. 173.
[4] R. P. Meilanov and M. S. Yanpolov, “Features of the Phase Trajectory of a Fractal Oscillator,” Technical Physics Letters, Vol. 28, No. 1, 2002, pp. 67-73. doi:10.1134/1.1448634
[5] R. I. Parovik, “Cauchy Problem for Non Local Mathieu Equation,” Doklady AMAN, Vol. 13, No. 2, 2011, pp. 90-98.
[6] F. Van de Pol and M. J. Strutt, “On the Stability of the Solutions of Mathieu’s Equation,” Philosophical Magazine, Vol. 5, 1928, pp. 18-38.
[7] R. H. Rand, S. M. Sah and M. K. Suchrsky, “Fractional Mathieu Equation,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, 2010, pp. 3254-3262.
[8] V. V. Afanas’ev and M. J. E. Daniel, “Polish Stabilization of the Inertial Effects of the Fractal Oscillator,” Technical Physics Letters, Vol. 36, No. 7, 2010, pp. 1-6.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.