Acta Mechanica Slovaca 2016, 20(2):62-69 | DOI: 10.21496/ams.2016.016

Modeling of Transient Nonlinear Phenomena using a Modified Logistic Equation

Tomáš Stejskal*, Jozef Svetlík, Peter Demeč, Ľuboslava Šidlovská
Technical University of Košice, Faculty of Mechanical Engineering, Department of Production Technique, Letná 9, 040 00 Košice, Slovakia

The paper deals with modelling of nonlinear transient responses that occur in the technical and natural objects. In the field of non-linear phenomena are generated structures that have regular and chaotic nature. As a modelling tool, we used a modification of the logistic equation. Search and display of various structures was achieved when using parameter iterations of modified logistic equation. An iterative method in this case appears to be a very effective tool. The novelty of the method is in creating regular and chaotic structures in the time development of nonlinear functions.

Keywords: nonlinear dynamic, logistic map, logistic function, chaos

Published: October 31, 2016  Show citation

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Stejskal, T., Svetlík, J., Demeč, P., & Šidlovská, Ľ. (2016). Modeling of Transient Nonlinear Phenomena using a Modified Logistic Equation. Acta Mechanica Slovaca, 20(2), 62-69. doi: 10.21496/ams.2016.016
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    References

    1. VANAG, Vladimir K.; EPSTEIN, Irving R. Pattern formation in a tunable medium: The Belousov-Zhabotinsky reaction in an aerosol OT microemulsion. Physical review letters, 2001, 87.22: 228301. Go to original source...
    2. KLYUCHEVSKII, Anatoly V.; KHLEBOPROS, Rem G. Coupled large earthquakes in the Baikal rift system: Response to bifurcations in nonlinear resonance hysteresis. Geoscience Frontiers, 2013, 4.6: 709-716. Go to original source...
    3. HOU, Dongxiao; PENG, Rongrong; LIU, Haoran. Analysis of vertical-horizontal coupling vibration characteristics of rolling mill rolls based on strip dynamic deformation process. Shock and Vibration, 2014, 2014. Go to original source...
    4. DOMBOVARI, Zoltan; STEPAN, Gabor. On the bistable zone of milling processes. Phil. Trans. R. Soc. A, 2015, 373.2051: 20140409. Go to original source...
    5. DOMBOVARI, Zoltan; WILSON, R. Eddie; STEPAN, Gabor. Estimates of the bistable region in metal cutting. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 2008. p. 3255-3271. Go to original source...
    6. DOMOKOS, G.; HOLMES, P. Euler's problem, Euler's method, and the standard map; or, the discrete charm of buckling. Journal of Nonlinear Science, 1993, 3.1: 109-151. Go to original source...
    7. SHINBROT, Troy, et al. Chaos in a double pendulum. Am. J. Phys, 1992, 60.6: 491-499. Go to original source...
    8. SZUMINSKI, Wojciech Dynamics of multiple pendula without gravity : Chaotic Modeling and Simulation - CMSIM.- 2014, no. 1, pp. 57-67
    9. FEIGENBAUM, Mitchell J. Quantitative universality for a class of nonlinear transformations. Journal of statistical physics, 1978, 19.1: 25-52. Go to original source...
    10. ČAČKO, Peter; KRENICKÝ, Tibor. Impact of Lubrication Interval to Operating Status of Bearing. In: Applied Mechanics and Materials. Trans Tech Publications, 2014. p. 151-158. Go to original source...

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