期刊
PHYSICAL REVIEW LETTERS
卷 91, 期 3, 页码 -出版社
AMERICAN PHYSICAL SOC
DOI: 10.1103/PhysRevLett.91.034101
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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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