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

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

1997-09-08

arxiv.org/abs/chao-dyn/9709007v1

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1103/PhysRevE.56.6451

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.

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