Chaotic recurrence enables a simpler method for calculating phase boundaries
Chaotic recurrence enables a simpler method for calculating phase boundaries lead image
The swirling patterns of chaotic phase diagrams are alluring, but they provide only a coarse overview of a chaotic map’s inner structure. One such map — the standard nontwist map, or SNM — has been used to describe the physics of many systems, from the structure of magnetic field lines in tokamak reactors to plasma dynamics in the Earth’s magnetosphere. The SNM features boundaries in phase space that block trajectories from exploring the full expanse of the phase diagram, but it can be time-consuming to map out the parameters for which these boundaries emerge or break apart.
A new technique reported by Santos et al. provides a more efficient method for determining these parameters in the SNM, reducing the number of required map iterations by a factor of 100. The technique relies on a particular analysis of the SNM called the recurrence plot, which picks out the phase space points that trace out close-by orbits under the action of the map.
Diagonal lines in the recurrence plot signify regions in phase space that are more predictable. By looking at the distribution of diagonal lines in the SNM’s recurrence plot — a measure known as the determinism — and calculating the standard deviation, the authors were able to estimate the SNM parameters for which barriers appear and break up.
Additionally, the determinism measure allowed the team to spot areas in the map where bifurcations occurred, which were missed by previous methods. The new technique could extend to other chaotic maps and may even help in the study of plasma confinement times in fusion reactors, according to author Antonio Batista.
Source: “Recurrence-based analysis of barrier breakup in the standard nontwist map,” by Moises S. Santos, Michele Mugnaine, Jose D. Szezech Jr., Antonio M. Batista, Iberê L. Caldas, Murilo S. Baptista, and Ricardo L. Viana, Chaos: An Interdisciplinary Journal of Nonlinear Science (2018). The article can be accessed at https://doi.org/10.1063/1.5021544 .
