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Chaotic dynamics of the fractional Lorenz system
Ilia Grigorenko1, Elena Grigorenko
1Institut für Theoretische Physik der Freien Universität Berlin, Arnimallee 14, 14195 Berlin, Germany.
Physical Review Letters
|August 9, 2003
Abstract:
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.