Volume 20, Issue No.2


nonlinear dynamic, logistic map, logistic function, chaos


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.


Acta Mechanica Slovaca. Volume 20, Issue 2, Pages 62 – 69, ISSN 1335-2393


  Modeling of Transient Nonlinear Phenomena using a Modified Logistic Equation


[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.
[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.
[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.
[4] DOMBOVARI, Zoltan; STEPAN, Gabor. On the bistable zone of milling processes. Phil. Trans. R. Soc. A, 2015, 373.2051: 20140409.
[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.
[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.
[7] SHINBROT, Troy, et al. Chaos in a double pendulum. Am. J. Phys, 1992, 60.6: 491-499.
[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.
[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.

Latest Issue

ams 2 2016