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Triple mode alignment in a canonical model of the blue-sky catastrophe

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Abstract

The blue-sky catastrophe (BSC) is a homoclinic bifurcation of a saddle node periodic orbit of codimension one, which has been found to occur in a number of physically relevant dynamics systems. The onset and termination of the BSC in a chaotic system is shown to coincide with the occurrence of triple mode alignment in a canonical model undergoing the BSC when the model is recast as an oscillator system. Typically, such behavior is only seen in hyperchaotic systems of dimension greater than three. Hence, in the case of three dimensional chaotic systems, competitive modes may under some circumstances be used in the prediction of the blue-sky catastrophe. Limitations to this approach are also discussed.

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Acknowledgements

R.A.V. was supported in part by NSF grant # 1144246.

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  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816-1364, USA

    Robert A. Van Gorder

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  1. Robert A. Van Gorder
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Correspondence to Robert A. Van Gorder.

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Van Gorder, R.A. Triple mode alignment in a canonical model of the blue-sky catastrophe. Nonlinear Dyn 73, 397–403 (2013). https://doi.org/10.1007/s11071-013-0794-y

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  • DOI: https://doi.org/10.1007/s11071-013-0794-y

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