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

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
8 Downloads (Pure)


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
Issue number8
Early online date28 Aug 2018
Publication statusPublished - Aug 2018

Bibliographical note

We wish to acknowledge the support: CNPq, CAPES, and FAPESP.


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