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Synchronization of chaotic fractional Chen system. (English) Zbl 1080.34537
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 $$u\in \mathbb{R}$$ 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 $$q_3=0.86$$.
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.

##### MSC:
 34D05 Asymptotic properties of solutions to ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 26A33 Fractional derivatives and integrals
##### Keywords:
fractional derivative; Chen’s system; synchronization
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