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Zbl 1131.34040
Wu, Xiaofeng; Chen, Guanrong; Cai, Jianping
Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control.
(English)
[J] Physica D 229, No. 1, 52-80 (2007). ISSN 0167-2789

The paper provides sufficient conditions for the synchronization of coupled systems of ordinary differential equations $$\dot x = g(x), \quad \dot y = g(y) +K(x-y),$$ with $y,z\in \Bbb R^3$, and where $g(\cdot)$ represents the right-hand side of the generalized Lorenz system, $K$ is the coupling matrix. Synchronization is considered here in a local sense, i.e. $\Vert x-y \Vert \to 0$ as $t\to\infty$ for all sufficiently close initial conditions $x(0)$, $y(0)$. The main tools are linearization and Lyapunov functions.
[Sergiy Yanchuk (Berlin)]
MSC 2000:
*34D05 Asymptotic stability of ODE
34C15 Nonlinear oscillations of solutions of ODE
34C28 Other types of "recurrent" solutions of ODE

Keywords: Chaos; Synchronization; Generalized Lorenz system; Linear state error feedback control

Cited in: Zbl 1226.93063

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