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Basin bifurcation in quasiperiodically forced systems

Ulrike Feudel1, Annette Witt1, Ying-Cheng Lai2, and Celso Grebogi1,3

  • 1Institut für Physik, Universität Potsdam, Am Neuen Palais, PF 601553, D-14415, Potsdam, Germany
  • 2Departments of Physics and Astronomy and of Mathematics, The University of Kansas, Lawrence, Kansas 66045
  • 3Institute for Plasma Research, University of Maryland, College Park, Maryland 20742

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Phys. Rev. E 58, 3060 – Published 1 September, 1998

DOI: https://doi.org/10.1103/PhysRevE.58.3060

Abstract

In this paper we study quasiperiodically forced systems exhibiting fractal and Wada basin boundaries. Specifically, by utilizing a class of representative systems, we analyze the dynamical origin of such basin boundaries and we characterize them. Furthermore, we find that basin boundaries in a quasiperiodically driven system can undergo a unique type of bifurcation in which isolated “islands” of basins of attraction are created as a system parameter changes. The mechanism for this type of basin boundary bifurcation is elucidated.

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References (29)

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Phys. Rev. E 58, 3060– Published 1 September, 1998
  • Received 2 February 1998

© 1998 American Physical Society

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