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arXiv · 1802.10539

From synchronous to one-time delayed dynamics in coupled maps

Celia Anteneodo·Juan Carlos Gonzalez-Avella·Raul O. Vallejos
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Abstract

We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($α$), that can vary from first-neighbors to global coupling, and a parameter ($β$) that allows to scan continuously from non-delayed to one-time delayed dynamics. % We identify in the plane $α$-$\varepsilon$ periodic orbits, limit cycles and chaotic trajectories, and describe how these structures change with the delay. These features can be explained by studying the bifurcation diagrams of a two-dimensional non-delayed map. This allows us to understand the effects of one-time delays on CSSs, e.g, regularization of chaotic orbits and synchronization of short-range coupled maps, observed when the dynamics is moderately delayed. Finally, we substitute the logistic map by cubic and logarithmic maps, in order to test the robustness of our findings.

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Celia Anteneodo, Juan Carlos Gonzalez-Avella, Raul O. Vallejos. 2018-02-28. From synchronous to one-time delayed dynamics in coupled maps. https://doi.org/10.1103/physreve.95.062213

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