Can We Obtain a Fractional Lorenz System from a Physical Problem？  

作　　者：杨帆 朱克勤 

机构地区：[1]Department of Engineering Mechanics, Tsinghua University, Beijing 100084

出　　处：《Chinese Physics Letters》2010年第12期124-127,共4页中国物理快报（英文版）

基　　金：Supported by the National Natural Science Foundation of China under Grant No 10972117.

摘　　要：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 ∑, we find a critical value of the effective dimension ∑cr1, at which the solution of the system undergoes a transition from the chaotic motion to the periodic motion and another critical value ∑cr2（∑cr2 〈∑cr1） 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 ∑ is found to delay the onset of it.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 ∑, we find a critical value of the effective dimension ∑cr1, at which the solution of the system undergoes a transition from the chaotic motion to the periodic motion and another critical value ∑cr2（∑cr2 〈∑cr1） 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 ∑ is found to delay the onset of it.

关 键 词：Fluid dynamics Statistical physics and nonlinear systems 

分 类 号：O415.5[理学—理论物理] O4-4[理学—物理]