|Paper title:||Study of Complexities in Bouncing Ball Dynamical System|
|Published in:||Issue 1, (Vol. 10) / 2016Download|
|Author(s):||SAHA Lal Mohan, SARMA Til Prasad, DIXIT Purnima|
|Abstract.||Evolutionary motions in a bouncing ball system consisting of a ball having a free fall in the Earth’s gravitational field have been studied systematically. Because of nonlinear form of the equations of motion, evolutions show chaos for certain set of parameters for certain initial conditions. Bifurcation diagram has been drawn to study regular and chaotic behavior. Numerical calculations have been performed to calculate Lyapunov exponents, topological entropies and correlation dimension as measures of complexity. Numerical results are shown through interesting graphics.|
|Keywords:||Chaos, Lyapunov Exponents, Bifurcation, Topological Entropy|
|References:||1. Ian Stewart. Does God Play Dice ?, Penguin Books 1989
2. Adler, R L Konheim, A G McAndrew, M H. Topological entropy, Trans. Amer. Math. Soc. 1965; 114: 309-319
3. R. Bowen, R . Topological entropy for noncompact sets, Trans. Amer. Math. Soc. 1973: 184: 125-136
4. Holmes PJ. The dynamics of repeated impacts with a sinusoidally vibrating table. J Sound Vib 1982;84:173–89.
5. Everson RM. Chaotic dynamics of a bouncing ball. Physica D 1986;19:355–83.
6. Mello TM, Tuffilaro NM. Strange attractors of a bouncing ball. Am J Phys 1987;55:316–20.
7. Kini A, Vincent TL, Paden B. The bouncing ball apparatus as an experimental tool. J Dyn Syst Meas Control 2006;128:330–40.
8. Sebastian Vogel, Stefan J. Linz, Regular and chaotic dynamics in bouncing ball models. International Journal of Bifurcation and Chaos, Vol. 21, No. 3, 2011: 869–884
9. Litak G, Syta A, Budhraja M, Saha, L M. Detection of the chaotic behaviour of a bouncing ball by the 0–1 test. Chaos, Solitons and Fractals 42, 2009: 1511–1517
10. Grassberger P, Procaccia I. Measuring the Strangeness of Strange Attractors, Physica 9D, 1983:189-208.
11. Martelli M. Introduction to Discrete Dynamical Systems and Chaos. John Wiley & Sons, Inc., 1999, New York.
12. Nagashima H, Baba Y . Introduction to Chaos: Physics and Mathematics of Chaotic Phenomena. Overseas Press India Private Limited, 2005.
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