| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Can We Obtain a Fractional Lorenz System from a Physical Problem? |
| YANG Fan, ZHU Ke-Qin |
| Department of Engineering Mechanics, Tsinghua University, Beijing 100084 |
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| Cite this article: |
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YANG Fan, ZHU Ke-Qin 2010 Chin. Phys. Lett. 27 124701 |
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Abstract A new fractional-order Lorenz system is obtained from the convection of fractional Maxwell fluids in a circular loop. This is the first fractional-order dynamical system derived from an actual physical problem, and rich dynamical properties are observed. In the case of short fluid relaxation time, with the decreasing effective dimension Σ, we find a critical value of the effective dimension Σcr1, at which the solution of the system undergoes a transition from the chaotic motion to the periodic motion and another critical value Σcr2 (Σcr2 <Σcr1)at which the regular dynamics of the system returns to the chaotic one. In the case of long relaxation time, the phenomenon of overstability is observed and the decrease of Σ is found to delay the onset of it.
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| Keywords:
47.50.-d
46.35.+z
47.52.+j
05.45.Ac
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Received: 14 July 2010
Published: 23 November 2010
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| PACS: |
47.50.-d
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(Non-Newtonian fluid flows)
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46.35.+z
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(Viscoelasticity, plasticity, viscoplasticity)
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47.52.+j
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(Chaos in fluid dynamics)
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05.45.Ac
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(Low-dimensional chaos)
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[1] Lorenz E N 1963 J. Atmos. Sci. 20 130
[2] Tritton D J 1988 Physical Fluid Dynamics (Oxford: Clarendon)
[3] Yang F and Zhu K-Q 2010 Chin. Phys. Lett. 27 034601
[4] Grigorenko I et al 2003 Phys. Rev. Lett. 91 034101
[5] Hilfer R 2000 Applications of Fractional Calculus in Physics (Singapore: World Scientific)
[6] Schiessel H et al 1995 J. Phys. A 28 6567
[7] Friedrich C 1991 Rheol Acta 30 151
[8] Hernández-Jiménez A et al 2001 Polym. Test. 21 325
[9] Podlubny I 1999 Fractional Differential Equations (Orlando: Academic)
[10] Caputo M 1967 Geophys. J. R. Astron. Soc. 13 529
[11] Diethelm K et al 2002 Nonlinear Dynamics 29 3
[12] Li C and Peng G 2004 Chaos, Solitons and Fractals 22 443
[13] Khayat R E 1994 J. Non-Newtonian Fluid Mech. 53 227
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