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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.

34D05 Asymptotic properties of solutions to ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
26A33 Fractional derivatives and integrals
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