一类简单而复杂的单参数广义Lorenz-Like系统
A simple yet complex one-parameter family of generalized lorenz-like systems
摘要：
本文发现了一类简单的单参数三维二次自治混沌系统。通过调节唯一的参数，该系统可以连续地产生各种级联的类Lorenz吸引子，这似乎比包含Lorenz和Chen系统作为其两个极端的统一混沌系统更丰富。虽然这个新的混沌系统家族具有非常丰富和复杂的动力学，但它具有非常简单的代数结构，只有两个二次项（与Lorenz和Chen系统相同），线性部分中的所有非零系数都是-1，除了一个-0.1（因此，比Lorenz和Chen系统简单）。令人惊讶的是，虽然这个新系统属于现有分类中的Lorenz型系统家族，如广义Lorenz标准型，但它不仅可以产生Lorenz型吸引子，而且可以产生Chen型吸引子。这表明，可能存在一些其他的未知的，但更重要的代数特征分类一般的三维二次自治混沌系统。
英文摘要：
This paper reports the finding of a simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. By tuning the only parameter, this system can continuously generate a variety of cascading Lorenz-like attractors, which appears to be richer than the unified chaotic system that contains the Lorenz and the Chen systems as its two extremes. Although this new family of chaotic systems has very rich and complex dynamics, it has a very simple algebraic structure with only two quadratic terms (same as the Lorenz and the Chen systems) and all nonzero coefficients in the linear part being -1 except one -0.1 (thus, simpler than the Lorenz and Chen systems). Surprisingly, although this new system belongs to the family of Lorenz-type systems in some existing classifications such as the generalized Lorenz canonical form, it can generate not only Lorenz-like attractors but also Chen-like attractors. This suggests that there may exist some other unknown yet more essential algebraic characteristics for classifying general three-dimensional quadratic autonomous chaotic systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
