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Border collision bifurcations in one-dimensional linear-hyperbolic maps

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  • Gardini, Laura
  • Tramontana, Fabio
  • Sushko, Iryna

Abstract

In this paper we consider a continuous one-dimensional map, which is linear on one side of a generic kink point and hyperbolic on the other side. This kind of map is widely used in the applied context. Due to the simple expression of the two functions involved, in particular cases it is possible to determine analytically the border collision bifurcation curves that characterize the dynamic behaviors of the model. In the more general model we show that the steps to be performed are the same, although the analytical expressions are not given in explicit form.

Suggested Citation

  • Gardini, Laura & Tramontana, Fabio & Sushko, Iryna, 2010. "Border collision bifurcations in one-dimensional linear-hyperbolic maps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 899-914.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:4:p:899-914
    DOI: 10.1016/j.matcom.2010.10.001
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    References listed on IDEAS

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    1. Sushko, Iryna & Agliari, Anna & Gardini, Laura, 2006. "Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 756-770.
    2. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical dynamics and economics," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 37-83, July.
    3. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical Dynamics and Economics," Working Paper Series 293, Research Institute of Industrial Economics.
    4. Gardini, Laura & Sushko, Iryna & Naimzada, Ahmad K., 2008. "Growing through chaotic intervals," Journal of Economic Theory, Elsevier, vol. 143(1), pages 541-557, November.
    5. Zhusubaliyev, Zhanybai T. & Soukhoterin, Evgeniy & Mosekilde, Erik, 2007. "Quasiperiodicity and torus breakdown in a power electronic dc/dc converter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(6), pages 364-377.
    6. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, June.
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    Cited by:

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