Study of Bifurcations in 2-D Piecewise Smooth Discontinuous Maps

Maity, Dibyajyoti (2013) Study of Bifurcations in 2-D Piecewise Smooth Discontinuous Maps. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MS Dissertation of Dibyajyoti Maity) Dibyajyoti_Maity-08MS01-MS_Thesis.pdf Restricted to Repository staff only Download (7MB)

Abstract

There are systems, which yield piecewise smooth maps under stroboscopic sampling. A new class of bifurcations occur in such systems when a fixed point crosses the border between the smooth regions in the state space. As an extension, there exist a large number of switching dynamical systems that have been found to yield two-dimensional piecewise smooth maps that are discontinuous across the border. We perform a systematic analysis of the bifurcation phenomena in two-dimensional discontinuous maps through a normal form: the piecewise linear approximation in the neighbourhood of the border. We show that there can be many qualitatively different types of border collision bifurcations, depending on the parameters of the normal form. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur.

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