×

zbMATH — the first resource for mathematics

Combination synchronization of three classic chaotic systems using active backstepping design. (English) Zbl 1317.93114
Summary: In this paper, an active backstepping design is proposed to achieve combination synchronization between three different chaotic systems: Lorenz system, Chen’s system, and Lü system. The proposed method is a systematic design approach and consists in a recursive procedure that interlaces the choice of a Lyapunov function with the design of active control. Numerical simulations are shown to verify the feasibility and effectiveness of the proposed control technique.{
©2011 American Institute of Physics}

MSC:
93B51 Design techniques (robust design, computer-aided design, etc.)
34D06 Synchronization of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
93D30 Lyapunov and storage functions
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019
[2] DOI: 10.1103/PhysRevLett.76.1816
[3] DOI: 10.1103/PhysRevLett.76.1804
[4] DOI: 10.1103/PhysRevE.59.R6247
[5] DOI: 10.1088/0031-8949/78/01/015007 · Zbl 1157.37310
[6] DOI: 10.1103/PhysRevLett.82.3042
[7] DOI: 10.1103/PhysRevLett.76.1816
[8] DOI: 10.1016/j.chaos.2005.12.009 · Zbl 1134.37331
[9] DOI: 10.1103/PhysRevLett.64.1196 · Zbl 0964.37501
[10] DOI: 10.1016/j.cnsns.2008.06.018 · Zbl 1221.93224
[11] DOI: 10.1016/j.na.2008.10.069 · Zbl 1171.34324
[12] DOI: 10.1016/j.physleta.2005.06.020 · Zbl 1194.34090
[13] DOI: 10.1016/j.physleta.2006.08.067 · Zbl 1236.93086
[14] DOI: 10.1016/j.cnsns.2007.09.002 · Zbl 1221.93246
[15] DOI: 10.1016/j.chaos.2006.04.003 · Zbl 1129.93489
[16] Vaněčk A., Control Systems: From Linear Analysis to Synthesis of Chaos (1996)
[17] DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 · Zbl 1417.37129
[18] DOI: 10.1142/S0218127499001024 · Zbl 0962.37013
[19] DOI: 10.1142/S0218127402004620 · Zbl 1063.34510
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.