Influence of a square-root singularity on the behaviour of piecewise smooth maps

We consider a one-dimensional continuous piecewise smooth nonlinear map with square-root singularity. For particular choice of the parameters, this map represents the normal form of discrete-time representation of impact oscillator near grazing bifurcation. Owing to the nonlinearity, the map exhibit...

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Bibliographic Details
Published in:Nonlinearity 2010-02, Vol.23 (2), p.445-463
Main Authors: Avrutin, Viktor, Dutta, Partha Sharathi, Schanz, Michael, Banerjee, Soumitro
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical methods in physics
Mathematics
Other topics in mathematical methods in physics
Physics
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:We consider a one-dimensional continuous piecewise smooth nonlinear map with square-root singularity. For particular choice of the parameters, this map represents the normal form of discrete-time representation of impact oscillator near grazing bifurcation. Owing to the nonlinearity, the map exhibits smooth and nonsmooth bifurcations very closely related to each other. Our main aim is to study how the nonlinearity influences the known results of nonsmooth bifurcations and the interaction between smooth and nonsmooth bifurcations considering the whole parameter space. We also explain the organizing source of several atypical bifurcation phenomena using the concept of multi-parametric bifurcation.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/23/2/012