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Zbl 1080.34537
Deng, Weihua; Li, Changpin
Synchronization of chaotic fractional Chen system.
(English)
[J] J. Phys. Soc. Japan 74, No. 6, 1645-1648 (2005). ISSN 0031-9015; ISSN 1347-4073/e

The complete synchronization of two coupled Chen's systems with fractional derivatives is studied. The driven Chen's system has the form $$\frac{d^{q_1}x_m}{dt^{q_1}} = a(y_m-x_m),$$ $$\frac{d^{q_2}y_m}{dt^{q_2}} = (c-a)x_m -x_m z_m +c y_m,$$ $$\frac{d^{q_3}z_m}{dt^{q_3}} = x_m y_m -b z_m,$$ the response system reads $$\frac{d^{q_1}x_s}{dt^{q_1}} = a(y_s-x_s),$$ $$\frac{d^{q_2}y_s}{dt^{q_2}} = (c-a)x_s -x_m z_s +c y_s + u(y_s-y_m),$$ $$\frac{d^{q_3}z_s}{dt^{q_3}} = x_m y_s -b z_s,$$ where $u\in \bbfR$ is a control parameter, $(x_m,y_m,z_m)$ and $(x_s,y_s,z_s)$ are phase variables for the drive and response systems, respectively. $d^{q_i}/dt^{q_i}, i=1,2,3$, are the fractional derivatives with $q_1=0.86$, $q_2=0.88$, and $q_3=0.86$. \par Using Laplace transform theory, the authors provide conditions for synchronization. The technique given in the paper can be used to study synchronization of other systems with fractional derivatives.
[Sergiy Yanchuk (Berlin)]
MSC 2000:
*34D05 Asymptotic stability of ODE
34C15 Nonlinear oscillations of solutions of ODE
26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional derivative; Chen's system; synchronization

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