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May  2004, 4(2): 457-464. doi: 10.3934/dcdsb.2004.4.457

Non-smooth pitchfork bifurcations

Paul Glendinning 1,

1. 

Department of Mathematics, UMIST, P.O. Box 88, Manchester M60 1QD, United Kingdom

Received  August 2002 Revised  May 2003 Published  February 2004

The bifurcations of strange nonchaotic attractors in quasi-periodically forced systems are poorly understood. A simple two-parameter example is introduced which unifies previous observations of non-smooth pitchfork bifurcations and blowout bifurcations of strange nonchaotic attractors. The corresponding bifurcation curves can be calculated analytically. The example shows how these bifurcations are organized around a codimension two point in parameter space.
Keywords: quasi-periodically forced oscillator, strange nonchaotic attractor., Pitchfork bifurcation.
Mathematics Subject Classification: 37C4.
Citation: Paul Glendinning. Non-smooth pitchfork bifurcations. Discrete & Continuous Dynamical Systems - B, 2004, 4 (2) : 457-464. doi: 10.3934/dcdsb.2004.4.457
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