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October  2010, 14(3): 961-976. doi: 10.3934/dcdsb.2010.14.961

Period increment cascades in a discontinuous map with square-root singularity

Partha Sharathi Dutta 1, and  Soumitro Banerjee 2,

1. 

Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur-721302, West Bengal, India
2. 

Department of Physical Sciences, Indian Institute of Science Education and Research, Mohanpur-741252, Nadia, West Bengal, India

Received  August 2009 Revised  April 2010 Published  July 2010

We consider a discontinuous map with square-root singularity, which is relevant to many physical systems. Such maps occur in modeling grazing-sliding bifurcations in switching dynamical systems, or if the Poincaré plane coincides with the switching plane. It is shown that there are notable differences in the bifurcation scenarios between this type of discontinuous map and a continuous map with square-root singularity. We determine the bifurcation structures and the scaling constant analytically. A different kind of period increment is observed, and the possibility of breakdown of period increment cascade is detected. Finally, we show that a system of piecewise smooth ordinary differential equations can exhibit the same type of bifurcation behavior.
Keywords: square-root singularity, Discontinuous map, border collision bifurcation, period increment..
Mathematics Subject Classification: Primary: 37E05, 37G15; Secondary: 39A1.
Citation: Partha Sharathi Dutta, Soumitro Banerjee. Period increment cascades in a discontinuous map with square-root singularity. Discrete and Continuous Dynamical Systems - B, 2010, 14 (3) : 961-976. doi: 10.3934/dcdsb.2010.14.961
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