In this work we propose the chaotic nonlinear Lü structure in quaternion form. Our new structure is high dimensional (9D). Highlights and qualities of this model are studied. Also, we present a novel king of quaternion synchronization. We call this new sort of synchronization “quaternion complete synchronization” (QCS). The idea of QCS did not consider in writing and has some unusual properties. Some organizations are conducted using the Lyapunov function to study QCS of two identical Lü attractors with quaternion variables. Numerical studies have shown the validity and accuracy of the analytical results of the control functions. Numerical studies also showed properties that distinguish QCS from the rest of the synchronization types that were previously studied.

在这项工作中，我们提出了四元数形式的混沌非线性Lü结构。我们的新结构是高维（9D）。研究了该模型的亮点和质量。此外，我们提出了一种新颖的四元数同步之王。我们称这种新的同步为“四元数完全同步”（QCS）。QCS的想法没有经过书面考虑，并且具有一些不同寻常的特性。一些组织使用Lyapunov函数来研究两个具有四元数变量的相同Lü吸引子的QCS。数值研究表明了控制功能分析结果的有效性和准确性。数值研究还显示出将QCS与之前研究的其余同步类型区分开的属性。