Recurrence-based analysis of barrier breakup in the standard nontwist map

Moises S. Santos, Michele Mugnaine, Jose D. Szezech Jr, Antonio M. Batista, Iberê L. Caldas, Murilo S. Baptista, Ricardo L. Viana

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Abstract

We study the standard nontwist map that describes the dynamic behaviour of magnetic field lines near a local minimum or maximum of frequency. The standard nontwist map has a shearless invariant curve that acts like a barrier in phase space. Critical parameters for the breakup of the shearless curve have been determined by procedures based on the indicator points and bifurcations of periodical orbits, a methodology that demands high computational cost. To determine the breakup critical parameters, we propose a new simpler and general procedure based on the determinism analysis performed on the recurrence plot of orbits near the critical transition. We also show that the coexistence of islands and chaotic sea in phase space can be analysed by using the recurrence plot. In particular, the measurement of determinism from the recurrence plot provides us with a simple procedure to distinguish periodic from chaotic structures in the parameter space. We identify an invariant shearless breakup scenario, as well as we show that recurrence plots are useful tools to determine the presence of periodic orbit collisions and bifurcation curves.
Original languageEnglish
Article number085717
Number of pages6
JournalChaos
Volume28
Issue number8
Early online date28 Aug 2018
DOIs
Publication statusPublished - Aug 2018

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Recurrence Plot
Standard Map
Breakup
Recurrence
Orbits
plots
Determinism
orbits
Phase Space
curves
Orbit
Bifurcation Curve
Invariant Curves
Local Minima
Coexistence
Periodic Orbits
Magnetic fields
Dynamic Behavior
Parameter Space
Computational Cost

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Santos, M. S., Mugnaine, M., Szezech Jr, J. D., Batista, A. M., Caldas, I. L., Baptista, M. S., & Viana, R. L. (2018). Recurrence-based analysis of barrier breakup in the standard nontwist map. Chaos, 28(8), [085717]. https://doi.org/10.1063/1.5021544

Recurrence-based analysis of barrier breakup in the standard nontwist map. / Santos, Moises S.; Mugnaine, Michele; Szezech Jr, Jose D.; Batista, Antonio M.; Caldas, Iberê L.; Baptista, Murilo S.; Viana, Ricardo L.

In: Chaos, Vol. 28, No. 8, 085717, 08.2018.

Research output: Contribution to journalArticle

Santos, MS, Mugnaine, M, Szezech Jr, JD, Batista, AM, Caldas, IL, Baptista, MS & Viana, RL 2018, 'Recurrence-based analysis of barrier breakup in the standard nontwist map', Chaos, vol. 28, no. 8, 085717. https://doi.org/10.1063/1.5021544
Santos MS, Mugnaine M, Szezech Jr JD, Batista AM, Caldas IL, Baptista MS et al. Recurrence-based analysis of barrier breakup in the standard nontwist map. Chaos. 2018 Aug;28(8). 085717. https://doi.org/10.1063/1.5021544
Santos, Moises S. ; Mugnaine, Michele ; Szezech Jr, Jose D. ; Batista, Antonio M. ; Caldas, Iberê L. ; Baptista, Murilo S. ; Viana, Ricardo L. / Recurrence-based analysis of barrier breakup in the standard nontwist map. In: Chaos. 2018 ; Vol. 28, No. 8.
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AB - We study the standard nontwist map that describes the dynamic behaviour of magnetic field lines near a local minimum or maximum of frequency. The standard nontwist map has a shearless invariant curve that acts like a barrier in phase space. Critical parameters for the breakup of the shearless curve have been determined by procedures based on the indicator points and bifurcations of periodical orbits, a methodology that demands high computational cost. To determine the breakup critical parameters, we propose a new simpler and general procedure based on the determinism analysis performed on the recurrence plot of orbits near the critical transition. We also show that the coexistence of islands and chaotic sea in phase space can be analysed by using the recurrence plot. In particular, the measurement of determinism from the recurrence plot provides us with a simple procedure to distinguish periodic from chaotic structures in the parameter space. We identify an invariant shearless breakup scenario, as well as we show that recurrence plots are useful tools to determine the presence of periodic orbit collisions and bifurcation curves.

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