Non-normal parameter blowout bifurcation: An example in a truncated mean-field dynamo model
نویسندگان
چکیده
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. @S1063-651X~97!00312-7#
منابع مشابه
Blowout bifurcations and the onset of magnetic dynamo action*
This paper numerically investigates the magnetohydrodynamic equations in three dimensions with periodic boundary conditions in a parameter range where a forced fluid flow is chaotic. It is found that the transition to dynamo action, whereby the magnetic field is sustained by interaction with the forced flow, is a blowout bifurcation. The blowout bifurcation is typified by bursting behavior, or ...
متن کاملTransverse instability for non-normal parameters
Suppose a smooth dynamical system has an invariant subspace and a parameter that leaves the dynamics in the invariant subspace invariant while changing the normal dynamics. Then we say the parameter is a normal parameter, and much is understood of how attractors can change with normal parameters. Unfortunately, normal parameters do not arise very often in practise. We consider the behaviour of ...
متن کاملTruncated Linear Minimax Estimator of a Power of the Scale Parameter in a Lower- Bounded Parameter Space
Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...
متن کاملDynamics of Axisymmetric Truncated Dynamo Models
S u m m a r y : An important question regarding the study of mean field dynamo models is how to make precise the nature of their underlying dynamics. This is difficult both because relatively little is known about the dynamical behaviour of infinite dimensional systems and also due to the numerical cost of studying the related partial differential equations. As a first step towards their unders...
متن کاملLarge-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation
In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...
متن کامل