Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps

Details Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps

2004-08-05

arxiv.org/abs/nlin/0408010v1

Nonlinear Sciences

Chaotic Dynamics

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

Scientific paper

10.1016/j.physa.2004.04.105

We report exact analytical expressions locating the $0\to1$, $1\to2$ and $2\to4$ 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.

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