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Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps

Paulo C. Rech·Marcus W. Beims·Jason A. C. Gallas
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Abstract

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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Paulo C. Rech, Marcus W. Beims, Jason A. C. Gallas. 2004-08-05. Naimark-Sacker Bifurcations in Linearly Coupled Quadratic Maps. https://doi.org/10.1016/j.physa.2004.04.105

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