Riddling and chaotic synchronization of coupled piecewise-linear Lorenz maps

M.C. Vergès, R.F. Pereira, S.R. Lopes, R.L. Viana and T. Kapitaniak

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 12, 2515-2525

Abstract: We investigate the parametric evolution of riddled basins related to synchronization of chaos in two coupled piecewise-linear Lorenz maps. Riddling means that the basin of the synchronized attractor is shown to be riddled with holes belonging to another basin in an arbitrarily fine scale, which has serious consequences on the predictability of the final state for such a coupled system. We found that there are wide parameter intervals for which two piecewise-linear Lorenz maps exhibit riddled basins (globally or locally), which indicates that there are riddled basins in coupled Lorenz equations, as previously suggested by numerical experiments. The use of piecewise-linear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins.

Keywords: Riddled basins; Chaotic synchronization; Lorenz map; Piecewise-linear map; Bungalow map; Coupled maps (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:12:p:2515-2525

DOI: 10.1016/j.physa.2009.02.015

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