Volume 126, Number 2, April 2019
|Number of page(s)||7|
|Published online||29 May 2019|
Two-parameter areal scaling in the Hénon map
1 Max-Planck Institute for the Physics of Complex Systems - Nöthnitzer Str. 38, 01187 Dresden, Germany
2 Instituto de Investigaciones Físicas, Campus Cota-Cota, Universidad Mayor de San Andrés - La Paz, Bolivia
3 Instituto de Altos Estudos da Paraíba - Rua Silvino Lopes 419-2502, 58039-190 João Pessoa, Brazil
4 Department of Physics of Complex Systems, Eötvös Loránd University - H-1117 Budapest, Hungary
5 Complexity Sciences Center - 9225 Collins Avenue Suite 1208, Surfside, FL 33154, USA
Received: 21 February 2019
Accepted: 15 April 2019
We study a bifurcation cascade whose proper unfolding requires tuning more than one parameter simultaneously. Specifically, we investigate metric properties of extended self-similar triangular areas observed recently in the control parameter space of flows (lasers and electronic circuits), and maps. Such areas are delimited by shrimplike stability islands, seem to arise in unbounded quantities, and to accumulate in narrow intervals of control parameters. Numerically, we find their asymptotic rate of accumulation to be unity. The asymptotic properties of triangle vertices and their centroids are also investigated.
PACS: 02.70.-c – Computational techniques; simulations / 02.70.Rr – General statistical methods
© EPLA, 2019
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