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Hyperchaotic control and periodic synchronization between two degenerate optical parametric oscillators are presented by mutual coupling parameter modulation, based on the nonlinear kinetic characteristic of degenerate optical parametric oscillator. Theoretical results show that the two degenerate optical parametric oscillators in hyperchaotic state can be controlled into periodic output by mutual couple, no matter whether the two degenerate optical parametric oscillators are identical. It is also shown that the periodic states can result in identical synchronization or anti-synchronization only in the case where the largest Lyapunov exponent of the system is negative. Thus synchronization type and evolution process of synchronization are determined by modulating coefficient and initial conditions.
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Keywords:
- controlling hyperchaos /
- periodic state synchronization /
- mutual coupling parameter modulation /
- degenerate optical parametric oscillators
[1] Yue L J, Shen K 2005 Acta Phys. Sin. 54 5671(in Chinese)[岳立娟、 沈 柯 2005 54 5671]
[2] Wang R, Shen K 2001 Chin. Phys. B 10 711
[3] Zhang S H, Shen K 2002 Chin. Phys. B 11 894
[4] Feng X Q, Shen K2005 Chin. Phys. B 14 1526
[5] Shahverdiev E M, Shore K A 2009 Opt. Commun. 282 3568
[6] Guo D M, Yang L Z, Wang A B, Zhang X J, Wang Y C 2009 Acta Phys. Sin. 58 8275(in Chinese)[郭东明、杨玲珍、王安邦、张秀娟、王云才 2009 58 8275]
[7] Zhang S H, Yang H, Qian X Z2004 Acta Phys. Sin. 53 3706(in Chinese)[张胜海、杨 华、钱兴中 2004 53 3706]
[8] Fan W H, Tian X J, Yu Y L, Chen J F, Luo H E 2006 Acta Phys. Sin. 55 5105 (in Chinese)[范文华、田小建、于永力、陈菊芳、罗红娥 2006 55 5105 ]
[9] Liu Y, Feng X, Zhang W, Liu X M 2009 Chin. Phys. B18 3318
[10] Oppo G L, Bramblla M, Lugiato L A 1994 Phys. Rev. A 49 2028
[11] Oppo G L, Bramblla M, Gamesasca D G, Gatti A, Lugiato L A 1994 J. Mod. Opt. 41 1151
[12] Valcarcel G J, Staliunas K, Eugenio R, Sanchez-Morcillo VJ 1996 Phys. Rev. A 54 1609
[13] Staliunas K 1995 J. Mod. Opt. 42 1261
[14] Pettiaux N P, Li R D, Mandel P 1989 Opt. Commun. 72 256
[15] Feng X Q, Shen K 2008 Chaos Solitons Fract. 35 506
[16] Feng X Q, Shen K 2005 Opt. Quantum Electron. 37 695
[17] Ramaswamy R 1997 Phys. Rev. E 56 7294
[18] Maria D S V, Allan J L, Michael A L 1992 Phys. Rev. E 46 R7359
[19] Rong H, Vaidya P G 1992 Phys. Rev. E 46 7387
[20] Woafo P, Kraenkel R A 2002 Phys. Rev. E 65 036225
[21] Yamapi R, Chabi O J B 2004 Int. J. Bifur. Chaos 14 171
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[1] Yue L J, Shen K 2005 Acta Phys. Sin. 54 5671(in Chinese)[岳立娟、 沈 柯 2005 54 5671]
[2] Wang R, Shen K 2001 Chin. Phys. B 10 711
[3] Zhang S H, Shen K 2002 Chin. Phys. B 11 894
[4] Feng X Q, Shen K2005 Chin. Phys. B 14 1526
[5] Shahverdiev E M, Shore K A 2009 Opt. Commun. 282 3568
[6] Guo D M, Yang L Z, Wang A B, Zhang X J, Wang Y C 2009 Acta Phys. Sin. 58 8275(in Chinese)[郭东明、杨玲珍、王安邦、张秀娟、王云才 2009 58 8275]
[7] Zhang S H, Yang H, Qian X Z2004 Acta Phys. Sin. 53 3706(in Chinese)[张胜海、杨 华、钱兴中 2004 53 3706]
[8] Fan W H, Tian X J, Yu Y L, Chen J F, Luo H E 2006 Acta Phys. Sin. 55 5105 (in Chinese)[范文华、田小建、于永力、陈菊芳、罗红娥 2006 55 5105 ]
[9] Liu Y, Feng X, Zhang W, Liu X M 2009 Chin. Phys. B18 3318
[10] Oppo G L, Bramblla M, Lugiato L A 1994 Phys. Rev. A 49 2028
[11] Oppo G L, Bramblla M, Gamesasca D G, Gatti A, Lugiato L A 1994 J. Mod. Opt. 41 1151
[12] Valcarcel G J, Staliunas K, Eugenio R, Sanchez-Morcillo VJ 1996 Phys. Rev. A 54 1609
[13] Staliunas K 1995 J. Mod. Opt. 42 1261
[14] Pettiaux N P, Li R D, Mandel P 1989 Opt. Commun. 72 256
[15] Feng X Q, Shen K 2008 Chaos Solitons Fract. 35 506
[16] Feng X Q, Shen K 2005 Opt. Quantum Electron. 37 695
[17] Ramaswamy R 1997 Phys. Rev. E 56 7294
[18] Maria D S V, Allan J L, Michael A L 1992 Phys. Rev. E 46 R7359
[19] Rong H, Vaidya P G 1992 Phys. Rev. E 46 7387
[20] Woafo P, Kraenkel R A 2002 Phys. Rev. E 65 036225
[21] Yamapi R, Chabi O J B 2004 Int. J. Bifur. Chaos 14 171
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