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Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control. (English) Zbl 1131.34040
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.

MSC:
34D05Asymptotic stability of ODE
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C28Complex behavior, chaotic systems (ODE)
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References:
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