The estimate of the ultimate bound for a dynamical system is an important problem, which is useful for chaos control and synchronization. In this paper, the estimated ultimate bound of a class of complex Lorenz systems is provided, which extends the parameter regions identified in the current literature on this problem. Based on these results, a kind of complex Lorenz-type systems is constructed, which might have many or infinitely many strange nonchaotic attractors, chaotic attractors, or an infinitely-many-scroll attractor.

中文翻译：

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一类复 Lorenz 系统的有界性

动态系统的最终界限的估计是一个重要的问题，它对于混沌控制和同步很有用。在本文中，提供了一类复杂洛伦兹系统的估计极限边界，它扩展了当前文献中关于该问题的参数区域。基于这些结果，构造了一种复杂的洛伦兹型系统，该系统可能具有许多或无限多个奇异的非混沌吸引子、混沌吸引子或无限多滚动吸引子。