Non-normal parameter blowout bifurcation: an example in a truncated mean field dynamo model

Abstract

We examine global dynamics and bifurcations occurring in a truncated model of a stellar mean field dynamo. This model has symmetry-forced invariant subspaces for the dynamics and we find examples of transient type I intermittency and blowout bifurcations to transient on-off intermittency, involving laminar phases in the invariant submanifold. In particular, our model provides examples of blowout bifurcations that occur on varying a non-normal parameter; that is, the parameter varies the dynamics within the invariant subspace at the same time as the dynamics normal to it. As a consequence of this we find that the Lyapunov exponents do not vary smoothly and the blowout bifurcation occurs over a range of parameter values rather than a point in the parameter space.

Full paper with figures, also available on the web page http://www.maths.qmw.ac.uk/~eoc. Physical Review E, accepted

References in corpus (1)

• Crisis-induced intermittency in truncated mean field dynamos

Cited by in corpus (7)

• Transverse instability for non-normal parameters
• Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection
• In--out intermittency in PDE and ODE models
• A novel type of intermittency in a nonlinear dynamo in a compressible flow
• The fratricide of alpha-Omega dynamos by their alpha-squared siblings
• The influence of noise on scalings for in-out intermittency
• Multiple forms of intermittency in PDE dynamo models