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Synchronization of unified chaotic system based on passive control. (English) Zbl 1119.34332
The paper studies the following control problem: Find a control function $$u=u(x,y)$$ such that two systems $$x'=f(x)$$ and $$y'=f(y)+u$$, where $$x,y \in \mathbb{R}^3$$ are synchronized, i.e. $$\| x(t,x_0)-y(t,y_0)\| \to 0$$ for any initial conditions $$x_0 = x(0,x_0)$$ and $$y_0=y(0,y_0)$$. The function $$f$$ is chosen to correspond to the so called unified chaotic system, although chaos is not a matter of the paper.

##### MSC:
 34H05 Control problems involving ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations
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##### References:
 [1] Pecora, L.M., Synchronization in chaotic systems, Phys. rev. lett., 64, 821-824, (1990) · Zbl 0938.37019 [2] Colet, P.; Roy, R., Digital communication with synchronized chaotic lasers, Opt. lett., 19, 2056, (1994) [3] Sugawara, T., Observation of synchronization in laser chaos, Phys. rev. lett., 72, 3502-3505, (1994) [4] Chen, H.-K., Global chaos synchronization of a new chaotic system via nonlinear control, Chaos solitons fractals, 23, 1245-1251, (2005) · Zbl 1102.37302 [5] Hong, Y.; Qin, H.; Chen, G.R., Adaptive synchronization of chaotic systems via state or output feedback control, Internat. J. bifur. chaos, 11, 1149-1158, (2001) · Zbl 1090.93535 [6] Park, J.H., Synchronization of Genesio chaotic system via backstepping approach, Chaos solitons fractals, 27, 1369-1375, (2006) · Zbl 1091.93028 [7] Li, C.D.; Xiao, X.F., Impulsive synchronization of chaotic systems, Chaos, (2005), 15-023104 [8] Agiza, H.N.; Yassen, M.T., Synchronization of rossler and Chen chaotic dynamical systems using active control, Phys. lett. A, 278, 191-197, (2000) · Zbl 0972.37019 [9] Wen, Y., Passive equivalence of chaos in Lorenz system, IEEE trans. circuits syst. I, 46, 876-878, (1999) [10] Qi, D.L.; Li, X.R.; Zhao, G.Z., Passive control of hybrid chaotic dynamical systems, J. zhejiang university (engineering science), 38, 86-89, (2004) [11] Lu, J.H.; Chen, G.R.; Cheng, D.; Celikovsky, S., Bridge the gap between the Lorenz system and the Chen system, Internat. J. bifur. chaos, 12, 2917-2926, (2002) · Zbl 1043.37026 [12] Lorenz, E.N., Deterministic nonperiodic flow, J. atmos. sci., 20, 130-141, (1963) · Zbl 1417.37129 [13] Chen, G.R.; Ueta, T., Yet another chaotic attractor, Internat. J. bifur. chaos, 9, 1465-1466, (1999) · Zbl 0962.37013 [14] Lu, J.H.; Chen, G.R., A new chaotic attractor coined, Internat. J. bifur. chaos, 12, 659-661, (2002) · Zbl 1063.34510
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