Can a Three-Dimensional Smooth Autonomous Quadratic Chaotic System Generate a Single Four-scroll Attractor?
Can a Three-Dimensional Smooth Autonomous Quadratic Chaotic System Generate a Single Four-scroll Attractor?
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DOI：
10.1142/s0218127404009880
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发表时间：
2004-04
期刊：
影响因子：
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通讯作者：
Wenbo Liu;Guanrong Chen
中科院分区：
文献类型：
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作者：
Wenbo Liu;Guanrong Chen
最近，我们研究了一个新的三维自治二次常微分方程的混沌系统，并发现该系统直观地显示了一个四涡卷混沌吸引子，数值模拟和电路实现证实。在本文中，我们进一步研究了以下问题：这是真的，该系统可以产生一个四涡卷混沌吸引子，或者它只是一个数值人工制品？通过沿着的理论分析和进一步的数值模拟，我们得出结论：我们在计算机和示波器上观测到的该系统的四涡卷混沌吸引子在理论上是不存在的。事实上，该系统具有两个共存的双涡卷混沌吸引子，它们在相空间中的位置对于某些系统参数是任意接近的，因此，极小的数值舍入误差或信号波动会促使系统轨道从一个吸引子切换到另一个吸引子，从而在屏幕上形成看似单一的四涡卷混沌吸引子.
Recently, we have investigated a new chaotic system of three-dimensional autonomous quadratic ordinary differential equations, and found that the system visually displays a four-scroll chaotic attractor confirmed by both numerical simulations and circuit implementation. In this paper, we further study the following question: Is it really true that this system can generate a four-scroll chaotic attractor, or is it only a numerical artifact? By a more careful theoretical analysis along with some further numerical simulations, we conclude that the four-scroll chaotic attractor of this system, which we observed on both computer and oscilloscope, cannot actually exist in theory. The fact is that this system has two co-existing two-scroll chaotic attractors that are arbitrarily close in the phase space for some system parameters, therefore extremely tiny numerical round-off errors or signal fluctuations will nudge the system orbit to switch from one attractor to another, thereby forming the seemingly single four-scroll chaotic attractor on screen display.