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Period three may not mean chaos: An example of a piecewise linear map

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Abstract

This paper presents an example of a piecewise linear map used to model the dynamics of certain nonlinear mechanical systems. It is shown that a period three solution exists, and computational study seems to indicate that it is a global attractor except possibly over a set of measure zero. The computations are performed using the cell mapping approach from both the deterministic and probabilistic points of view.

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References

  • Collet, P.; Eckmann, J. P. (1983): Iterated maps on the intervals as dynamical systems. Birkhäuser: Boston

    Google Scholar 

  • Guckenheimer, J.; Oster, G.; Ipaktchi, A. (1977): The dynamics of density dependent population models. J. Math. Biol. 4, 101–147

    Google Scholar 

  • Hsu, C. S. (1980): A theory of cell-to-cell mapping dynamical systems. J. Appl. Mech. 47, 931–939

    Google Scholar 

  • Hsu, C. S. (1981): A generalized theory of cell-to-cell mapping for nonlinear dynamical systems. J. Appl. Mech. 48, 634–642

    Google Scholar 

  • Hsu, C. S.; Guttalu, R. S. (1980): An unravelling algorithm for global analysis of dynamical systems: An application of cell-to-cell mappings. J. Appl. Mech. 47, 940–948

    Google Scholar 

  • Hsu, C. S.; Yee, H. C. (1975): Behavior of dynamical systems governed by a simple nonlinear difference equation. J. Appl. Mech. 42, 870–876

    Google Scholar 

  • Hsu, C. S.; Guttalu, R. S.; Zhu, W. H. (1982): A method of analyzing generalized cell mappings. J. Appl. Mech. 49, 895–904

    Google Scholar 

  • Li, T.; Yorke, J. A. (1975): Period three implies chaos. Am. Math. Month. 82, 985–992

    Google Scholar 

  • Singer, D. (1978): Stable orbits and bifurcation of maps of the interval. SIAM J. Appl. Math. 35, 260–267

    Google Scholar 

  • Straffin, P. D. (1978): Periodic points of continuous functions. Math. Mag. 51, 99–105

    Google Scholar 

  • Yorke, J. A.; Yorke, E. D. (1979): Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model. J. Stat. Phys. 21, 263–277

    Google Scholar 

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, University of Southern California, 90089, Los Angeles, CA, USA

    R. S. Guttalu & F. E. Udwadia

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  1. R. S. Guttalu
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  2. F. E. Udwadia
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Guttalu, R.S., Udwadia, F.E. Period three may not mean chaos: An example of a piecewise linear map. Computational Mechanics 5, 113–118 (1989). https://doi.org/10.1007/BF01046480

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  • DOI: https://doi.org/10.1007/BF01046480

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