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

J Laugesen,S P Kuznetsov,E Mosekilde,T Bountis

doi:10.1155/s1026022600000558

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.

Highlights

Many interesting phenomena have been discovered by studying the dynamics of weakly coupled, identical one-dimensional (l-D) maps
We have previously studied this phenomenon in detail and found that the strongly nonuniform reinjection process produced by the map (2.1) causes an anomaly in the statistics of the laminar phases [23]
The nonlinear scale serves to accentuate the variations during the laminar phases relative to the much larger excursions that take place during the turbulent bursts

Summary

Introduction

Many interesting phenomena have been discovered by studying the dynamics of weakly coupled, identical one-dimensional (l-D) maps. Coupled logistic [1,2,3] and coupled circle maps [4] have been extensively investigated from the point of view of the persistence of their bifurcation structures under the stabilizing or destabilizing influences of the mutual interaction. It was observed by Froyland [1], for instance, that the period-doubling route to chaos may be replaced by a quasiperiodic transition when two identical logistic maps are coupled symmetrically. Based on detailed analytic work, Reick and Mosekilde [7] were subsequently able to demonstrate that the behavior is generic to symmetrically coupled perioddoubling systems, and that it is robust towards slight deviations from complete symmetry

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Conclusion