Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps

Paulo C. Rech; Marcus W. Beims; Jason A. C. Gallas

doi:10.1016/j.physa.2004.04.105

paper

Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps

arXiv:nlin/0408010 · doi:10.1016/j.physa.2004.04.105

Abstract

We report exact analytical expressions locating the $0 \to 1$ , $1 \to 2$ and $2 \to 4$ bifurcation curves for a prototypical system of two linearly coupled quadratic maps. Of interest is the precise location of the parameter sets where Naimark-Sacker bifurcations occur, starting from a non-diagonal period-2 orbit. This result is the key to understand the onset of synchronization in networks of quadratic maps.

6 pages, 3 figures (1 in color), submitted to Physica A