Chaotic dynamics of the fractional Lorenz system

被引：625
|
作者：
Grigorenko, I
Grigorenko, E
机构：
[1] Free Univ Berlin, Inst Theoret Phys, D-14195 Berlin, Germany
[2] Irkutsk State Acad Econ, Irkutsk 664015, Russia
来源：
PHYSICAL REVIEW LETTERS | 2003年 / 91卷 / 03期
关键词：
D O I：
10.1103/PhysRevLett.91.034101
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this Letter we introduce a generalization of the Lorenz dynamical system using fractional derivatives. Thus, the system can have an effective noninteger dimension Sigma defined as a sum of the orders of all involved derivatives. We found that the system with Sigma<3 can exhibit chaotic behavior. A striking finding is that there is a critical value of the effective dimension Sigma(cr), under which the system undergoes a transition from chaotic dynamics to regular one.
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页数：4
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