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A ring network with fractional-order bistable oscillators is proposed, and the relationship between synchronization and parameters, such as coupling modes and the initial structural conditions, etc., is investigated. Based on the bistable characteristics of P-R oscillator, the effects of the coupling strength and the structures in initial conditions on the dynamic behaviors of the ring network are investigated by analyzing the largest conditional Lyapunov exponents, the largest Lyapunov exponents and the bifurcation diagrams, etc. Further investigation reveals that the ring network can be controlled to form chaotic synchronization, chaotic non-synchronization, synchronous amplitude death, synchronous non-amplitude death, etc. by changing the initial conditions and the coupling strength. Furthermore, the contours of the largest conditional Lyapunov exponents and the largest Lyapunov exponents also show how the dynamic behaviors of the network are influenced by the competition between couplings along directions of y and z, strongly relies on the initial structural conditions of network.
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Keywords:
- initial conditions /
- amplitude death /
- bistable states
[1] Lai Y C, Bollt E M, Liu Z H 2003 Chaos Solitons and Fractals 15 219
[2] [3] Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese) 张若洵, 杨世平 2009 58 2957]
[4] [5] Hasler M 1998 Int. J. Bifurcat. Chaos 8 647
[6] [7] Heagy J F, Pecora L M, Carroll T L 1995 Phys. Rev. Lett. 74 4185
[8] [9] Liu W Q, Qian X L, Yang J Z, Xiao J H 2006 Phys. Lett. A 354 119
[10] [11] Yamaguchi Y, Shimizu H 1984 Phycica D 11 212
[12] Yang J 2007 Phys. Rev. E 76 016204
[13] [14] Liu W Q, Xiao J H, Yang J Z 2005 Phys. Rev. E 72 057201
[15] [16] Prasad A 2005 Phy. Rev. E 72 056204
[17] [18] [19] Zhu Y, Qian X L, Yang J Z 2008 Europhys. Lett. 82 40001
[20] Mandelbrot B B 1983 The Fractal Geometiy of Nature (San Diego: W H Freeman Co)
[21] [22] Shao S Y, Min F H, Ma M L, Wang E R 2013 Acta Phys. Sin. 62 130504 (in Chinese) [邵书义, 闵富红, 马美玲, 王恩荣 2013 62 130504]
[23] [24] Jia H Y, Chen Z Q, Xue W 2013 Acta Phys. Sin. 62 140503 (in Chinese) [贾红艳, 陈增强, 薛薇 2013 62 140503]
[25] [26] Shao S Q, Gao X, Liu X W 2007 Acta Phys. Sin. 56 6815 (in chinese) [邵仕泉, 高心, 刘兴文 2007 56 6815]
[27] [28] [29] Deng W H, Li C P 2005 Physica A 353 61
[30] [31] Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣, 刘崇新, 王发强, 李永勋 2008 57 1416]
[32] [33] Yang S P, Zhang R X 2011 Chin. Phys. B 20 110506
[34] Gao X, Yu J B 2005 Chaos, Solitons and Fractals 26 141
[35] [36] Wang L M, Wu F 2013 Acta Phys. Sin. 62 210504 (in Chinese) [王立明, 吴峰 2013 62 210504]
[37] [38] Podlubny I 1999 Fractional Differential Equations (Vol. 198) (San Diego: Academic Press) p78
[39] [40] Pikovsky A S, Rabinovich M I 1978 Sov. Phys. Dokl. 23 183
[41] [42] Li C P, Peng G J 2004 Chaos, Solitons and Fractals 22 443
[43] -
[1] Lai Y C, Bollt E M, Liu Z H 2003 Chaos Solitons and Fractals 15 219
[2] [3] Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957 (in Chinese) 张若洵, 杨世平 2009 58 2957]
[4] [5] Hasler M 1998 Int. J. Bifurcat. Chaos 8 647
[6] [7] Heagy J F, Pecora L M, Carroll T L 1995 Phys. Rev. Lett. 74 4185
[8] [9] Liu W Q, Qian X L, Yang J Z, Xiao J H 2006 Phys. Lett. A 354 119
[10] [11] Yamaguchi Y, Shimizu H 1984 Phycica D 11 212
[12] Yang J 2007 Phys. Rev. E 76 016204
[13] [14] Liu W Q, Xiao J H, Yang J Z 2005 Phys. Rev. E 72 057201
[15] [16] Prasad A 2005 Phy. Rev. E 72 056204
[17] [18] [19] Zhu Y, Qian X L, Yang J Z 2008 Europhys. Lett. 82 40001
[20] Mandelbrot B B 1983 The Fractal Geometiy of Nature (San Diego: W H Freeman Co)
[21] [22] Shao S Y, Min F H, Ma M L, Wang E R 2013 Acta Phys. Sin. 62 130504 (in Chinese) [邵书义, 闵富红, 马美玲, 王恩荣 2013 62 130504]
[23] [24] Jia H Y, Chen Z Q, Xue W 2013 Acta Phys. Sin. 62 140503 (in Chinese) [贾红艳, 陈增强, 薛薇 2013 62 140503]
[25] [26] Shao S Q, Gao X, Liu X W 2007 Acta Phys. Sin. 56 6815 (in chinese) [邵仕泉, 高心, 刘兴文 2007 56 6815]
[27] [28] [29] Deng W H, Li C P 2005 Physica A 353 61
[30] [31] Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣, 刘崇新, 王发强, 李永勋 2008 57 1416]
[32] [33] Yang S P, Zhang R X 2011 Chin. Phys. B 20 110506
[34] Gao X, Yu J B 2005 Chaos, Solitons and Fractals 26 141
[35] [36] Wang L M, Wu F 2013 Acta Phys. Sin. 62 210504 (in Chinese) [王立明, 吴峰 2013 62 210504]
[37] [38] Podlubny I 1999 Fractional Differential Equations (Vol. 198) (San Diego: Academic Press) p78
[39] [40] Pikovsky A S, Rabinovich M I 1978 Sov. Phys. Dokl. 23 183
[41] [42] Li C P, Peng G J 2004 Chaos, Solitons and Fractals 22 443
[43]
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