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Self-synchronization of time delay implies that the synchronization between the time-delay system and the original system keeps the structure and parameters of systems unchanged, thus these various problems produced by time-delay in practice are avoided. Taking a time-delay complex Lorenz system for example, we investigate its dynamic characteristics and the influence of of time lag factor. A nonlinear feedback controller is designed to realize the self-synchronization of time delay of the complex Lorenz system. Numerical simulations verify the effectiveness of the presented controller. The controller adopts some states to realize the synchronization of all states. It is simple in principle and easy to implement in engineering.
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Keywords:
- time-delay system /
- complex chaotic systems /
- self-synchronization of time delay /
- Lyapunov exponent
[1] Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 62 018901]
[2] Ouyang C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese) [欧阳成, 林万涛, 程荣军, 莫嘉琪 2013 62 060201]
[3] Li C D, Liao X F 2004 Phys. Lett. A 329 301
[4] Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾, 徐伟 2007 56 3101]
[5] Mahmoud G M, Mahmoud E E 2012 Nonlinear Dyn. 67 1613
[6] Wang X Y, Zhang H 2013 Chin. Phys. B 22 048902
[7] Fowler A C, Gibbon J D 1982 Physica D 4 139
[8] Mahmoud G M, Bountis T, Mahmoud E E 2007 Internat. J. Bifur. Chaos 17 4295
[9] Luo C, Wang X Y 2013 Nonlinear Dyn. 71 241
[10] Luo C, Wang X Y 2013 Int. J. Mod. Phys. C 24 1350025
[11] Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 61 141
[12] Nian F Z, Wang X Y, Niu Y J, Lin D 2010 Appl. Math. Comput. 217 2481
[13] Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 62 875
[14] Liu S T, Liu P 2011 Nonlinear Anal. Real 12 3046
[15] Liu P, Liu S T 2011 Phys. Scr. 83 065006
[16] Mahmoud G M, Mahmoud E E 2010 Math. Comput. Simulat. 80 2286
[17] Liu P, Liu S 2012 Nonlinear Dyn. 70 585
[18] Zhu H 2011 ICCRD: 3rd Int. Conf. on Computer Research Development Shanghai, China, March 11–13, 2011 p451
[19] Liu P, Liu S T, Li X 2012 Phys. Scr. 85 035005
[20] Mahmoud E E 2013 Math. Comput. Simulat. 89 69
[21] Zhang F F, Liu S T, Yu W Y 2013 Chin. Phys. B 22 120505
[22] Gibbon J D, McGuinnes M J 1982 Physica D 5 108
[23] Ning C Z, Haken H 1990 Phys. Rev. A 41 3826
[24] Rauh A, Hannibal L, Abraham N 1996 Physica D 99 45
[25] Richter H 2001 Chaos Soliton. Fract. 12 2375
[26] Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[27] Hale J 1977 Theory of Functional Differential Equations (Vol. 3) (Berlin: Springer-Verlag) pp1–244
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[1] Liang Y, Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese) [梁义, 王兴元 2013 62 018901]
[2] Ouyang C, Lin W T, Cheng R J, Mo J Q 2013 Acta Phys. Sin. 62 060201 (in Chinese) [欧阳成, 林万涛, 程荣军, 莫嘉琪 2013 62 060201]
[3] Li C D, Liao X F 2004 Phys. Lett. A 329 301
[4] Jia F L, Xu W 2007 Acta Phys. Sin. 56 3101 (in Chinese) [贾飞蕾, 徐伟 2007 56 3101]
[5] Mahmoud G M, Mahmoud E E 2012 Nonlinear Dyn. 67 1613
[6] Wang X Y, Zhang H 2013 Chin. Phys. B 22 048902
[7] Fowler A C, Gibbon J D 1982 Physica D 4 139
[8] Mahmoud G M, Bountis T, Mahmoud E E 2007 Internat. J. Bifur. Chaos 17 4295
[9] Luo C, Wang X Y 2013 Nonlinear Dyn. 71 241
[10] Luo C, Wang X Y 2013 Int. J. Mod. Phys. C 24 1350025
[11] Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 61 141
[12] Nian F Z, Wang X Y, Niu Y J, Lin D 2010 Appl. Math. Comput. 217 2481
[13] Mahmoud G M, Mahmoud E E 2010 Nonlinear Dyn. 62 875
[14] Liu S T, Liu P 2011 Nonlinear Anal. Real 12 3046
[15] Liu P, Liu S T 2011 Phys. Scr. 83 065006
[16] Mahmoud G M, Mahmoud E E 2010 Math. Comput. Simulat. 80 2286
[17] Liu P, Liu S 2012 Nonlinear Dyn. 70 585
[18] Zhu H 2011 ICCRD: 3rd Int. Conf. on Computer Research Development Shanghai, China, March 11–13, 2011 p451
[19] Liu P, Liu S T, Li X 2012 Phys. Scr. 85 035005
[20] Mahmoud E E 2013 Math. Comput. Simulat. 89 69
[21] Zhang F F, Liu S T, Yu W Y 2013 Chin. Phys. B 22 120505
[22] Gibbon J D, McGuinnes M J 1982 Physica D 5 108
[23] Ning C Z, Haken H 1990 Phys. Rev. A 41 3826
[24] Rauh A, Hannibal L, Abraham N 1996 Physica D 99 45
[25] Richter H 2001 Chaos Soliton. Fract. 12 2375
[26] Wolf A, Swift J B, Swinney H L, Vastano J A 1985 Physica D 16 285
[27] Hale J 1977 Theory of Functional Differential Equations (Vol. 3) (Berlin: Springer-Verlag) pp1–244
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