From mandelbrot-like sets to arnold tongues - Endler A. (2013)
A transition from Mandelbrot-like sets to Arnold tongues is characterized via a coupling of two non-identical quadratic maps proposed by us. A two-dimensional parameter-space considering the parameters of the individual quadratic maps was used to demonstrate numerically the event. The location of the parameter sets where Naimark-Sacker bifurcations occur, which is exactly the place where Arnold tongues of arbitrary periods are born, was computed analytically. © 2013 Elsevier Ltd. All rights reserved.