标题： 耦合分段线性洛伦兹映射的弥漫同步和混沌同步 显示英文标题

标题： Riddling and chaotic synchronization of coupled piecewise-linear Lorenz maps

摘要： 我们研究了与两个耦合的分段线性洛伦兹映射混沌同步相关的riddled基底的参数演化。 riddled意味着同步吸引子的基底在任意精细尺度上被属于另一个基底的孔洞所填充，这对这种耦合系统的最终状态的可预测性有严重的影响。 我们发现存在广泛的参数区间，使得两个分段线性洛伦兹映射表现出riddled基底（全局或局部），这表明耦合洛伦兹方程中存在riddled基底，这之前通过数值实验已经有所建议。 使用分段线性映射使得可以严格证明riddled基底存在性的数学条件。 显示英文摘要

摘要： 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.