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Synchronization and chaos control in a periodically-forced, quasi-geostrophic, two-layer model of baroclinic instability

Eccles, Fiona and Read, Peter and Haine, Thomas (2006) Synchronization and chaos control in a periodically-forced, quasi-geostrophic, two-layer model of baroclinic instability. Nonlinear processes in geophysics, 13 (1). pp. 23-39.

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    Abstract

    Cyclic forcing on many timescales is believed to have a significant effect on various quasi-periodic, geophysical phenomena such as El Niño, the Quasi-Biennial Oscillation, and glacial cycles. This variability has been investigated by numerous previous workers, in models ranging from simple energy balance constructions to full general circulation models. We present a numerical study in which periodic forcing is applied to a highly idealised, two-layer, quasi-geostrophic model on a β-plane. The bifurcation structure and (unforced) behaviour of this particular model has been extensively examined by Lovegrove et al. (2001) and Lovegrove et al. (2002). We identify from their work three distinct regimes on which we perform our investigations: a steady, travelling wave regime, a quasi-periodic, modulated wave regime and a chaotic regime. In the travelling wave regime a nonlinear resonance is found. In the periodic regime, Arnol'd tongues, frequency locking and a Devil's staircase is seen for small amplitudes of forcing. As the forcing is increased the Arnol'd tongues undergo a period doubling route to chaos, and for larger forcings still, the parameter space we explored is dominated by either period 1 behaviour or chaotic behaviour. In the chaotic regime we extract unstable periodic orbits (UPOs) and add the periodic forcing at periods corresponding to integer multiples of the UPO periods. We find regions of synchronization, similar to Arnol'd tongue behaviour but more skewed and centred approximately on these periods. The regions where chaos suppression took place are smaller than the synchronization regions, and are contained within them.

    Item Type: Article
    Journal or Publication Title: Nonlinear processes in geophysics
    Additional Information: © Author(s) 2006. This work is licensed under a Creative Commons License.
    Subjects: R Medicine > R Medicine (General)
    Departments: Faculty of Health and Medicine > Health Research
    ID Code: 59962
    Deposited By: ep_importer_pure
    Deposited On: 12 Nov 2012 15:05
    Refereed?: Yes
    Published?: Published
    Last Modified: 10 Apr 2014 00:19
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/59962

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