Riddling and chaotic synchronization of coupled piecewise-linear Lorenz maps

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 the basin of infinity in an arbitrarily fine scale, what 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), what indicates that there are riddled basins in coupled Lorenz equations, as previously suggested by numerical experiments. The use of piecewiselinear maps makes it possible to prove rigorously the mathematical requirements for the existence of riddled basins.