Discrete Dynamics in Nature and Society 
Volume 5 (2000), Issue 3, Pages 233-245
doi:10.1155/S1026022600000558

Type-II intermittency in a class of two coupled one-dimensional maps

J. Laugesen,1 E. Mosekilde,1 T. Bountis,2 and S. P. Kuznetsov3

 1Department of Physics, The Technical University of Denmark, Lyngby 2800, Denmark
2Department of Mathematics, University of Patras, Patras 26110, Greece
3lnstitute of Radio-Engineering and Electronics, Russian Academy of Sciences, Zelenaya 38, Saratov 410019, Russia
Received 15 March 2000

Abstract

The paper shows how intermittency behavior of type-II can arise from the coupling of two one-dimensional maps, each exhibiting type-III intermittency. This change in dynamics occurs through the replacement of a subcritical period-doubling bifurcation in the individual map by a subcritical Hopf bifurcation in the coupled system. A variety of different parameter combinations are considered, and the statistics for the distribution of laminar phases is worked out. The results comply well with theoretical predictions. Provided that the reinjection process is reasonably uniform in two dimensions, the transition to type-II intermittency leads directly to higher order chaos. Hence, this transition represents a universal route to hyperchaos.