Non-smooth pitchfork bifurcations

Paul Glendinning

doi:10.3934/dcdsb.2004.4.457

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2004, Volume 4, Issue 2: 457-464. Doi: 10.3934/dcdsb.2004.4.457

This issue Previous Article Route to chaotic synchronisation in coupled map lattices: Rigorous results Next Article The long-time evolution of mean field magnetohydrodynamics

Non-smooth pitchfork bifurcations

Paul Glendinning^1,

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

Received: July 31, 2002

Revised: April 30, 2003

Published: April 2005

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Abstract

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.

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Mathematics Subject Classification: 37C45.

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