Adaptive full state hybrid projective synchronization of unified chaotic system with unknown parameters. (English) Zbl 1247.34095
Summary: This paper studies full state hybrid projective synchronization of the unified chaotic system with unknown parameters. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with unknown parameters asymptotically full state hybrid projective synchronized. Numerical simulations show the effectiveness of the scheme.
MSC:
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34H10 | Chaos control for problems involving ordinary differential equations |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 93C40 | Adaptive control/observation systems |
| 34D08 | Characteristic and Lyapunov exponents of ordinary differential equations |
Keywords:
the unified chaotic system; adaptive controller; unknown parameters; chaos synchronization; full state hybrid projective synchronizationReferences:
| [1] | DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019 · doi:10.1103/PhysRevLett.64.821 |
| [2] | X. Y. Wang, Chaos in the Complex Nonlinear Systems (Electronics Industry Press, Beijing, 2003) pp. 91–113. |
| [3] | X. P. Guan, Chaotic Control and Its Application on Secure Communication (National Defence Industry Press, Beijing, 2002) pp. 168–225. |
| [4] | DOI: 10.1103/PhysRevLett.85.5456 · doi:10.1103/PhysRevLett.85.5456 |
| [5] | DOI: 10.1016/S0960-0779(02)00585-4 · Zbl 1048.93508 · doi:10.1016/S0960-0779(02)00585-4 |
| [6] | DOI: 10.1016/S0960-0779(02)00006-1 · Zbl 1005.93020 · doi:10.1016/S0960-0779(02)00006-1 |
| [7] | DOI: 10.1103/PhysRevE.69.067201 · doi:10.1103/PhysRevE.69.067201 |
| [8] | Michael G. R., Phys. Rev. Lett. 76 pp 1804– |
| [9] | DOI: 10.1016/j.physleta.2007.04.102 · Zbl 1209.34076 · doi:10.1016/j.physleta.2007.04.102 |
| [10] | DOI: 10.1016/j.physleta.2007.09.051 · Zbl 1217.37037 · doi:10.1016/j.physleta.2007.09.051 |
| [11] | DOI: 10.1016/j.na.2007.02.009 · Zbl 1141.34030 · doi:10.1016/j.na.2007.02.009 |
| [12] | DOI: 10.1016/j.physleta.2006.01.039 · doi:10.1016/j.physleta.2006.01.039 |
| [13] | DOI: 10.1103/PhysRevLett.82.3042 · doi:10.1103/PhysRevLett.82.3042 |
| [14] | DOI: 10.1016/j.chaos.2004.02.019 · Zbl 1060.93530 · doi:10.1016/j.chaos.2004.02.019 |
| [15] | DOI: 10.1016/S0960-0779(04)00366-2 · doi:10.1016/S0960-0779(04)00366-2 |
| [16] | DOI: 10.1016/j.chaos.2004.09.117 · Zbl 1122.93311 · doi:10.1016/j.chaos.2004.09.117 |
| [17] | DOI: 10.1016/j.cnsns.2006.05.003 · Zbl 1123.37013 · doi:10.1016/j.cnsns.2006.05.003 |
| [18] | DOI: 10.1016/j.chaos.2005.02.008 · Zbl 1083.37514 · doi:10.1016/j.chaos.2005.02.008 |
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