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The dynamic behaviors of coupled fractional order bistable oscillators are investigated extensively and various phenomena such as synchronization, anti-synchronization, and amplitude death, etc. are explored. Based on the bistable characteristics of P-R oscillator with specific parameters, effects of initial conditions and coupling strength on the dynamic behaviors of the coupled fractional order bistable oscillators are first investigated by analyzing the maximum condition of Lyapunov exponent, the maximum Lyapunov exponent and the bifurcation diagram, etc. Further investigation reveals that the coupled fractional order bistable oscillators can be controlled to form chaotic synchronization, chaotic anti-synchronization, synchronous amplitude death, anti-synchronous amplitude death, partial amplitude death, and so on by changing the initial conditions and the coupling strength. Then, based on the principle of Monte Carlo method, by randomly choosing the initial conditions from the phase space, we calculate the percentage of various states when changing the coupling strength, so the dynamic characteristics of coupled fractional-order bistable oscillators can be represented by using the perspective of statistics. Some representative attractive basins are plotted, which are well coincident with numerical simulations.
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Keywords:
- amplitude death /
- attractive basin /
- bistable state
[1] Matthews P C, Strogatz S H 1990 Phys. Rev. Lett. 65 1701
[2] Ramana Reddy D V, Sen A, Johnston G L 1998 Phys. Rev. Lett. 80 5109
[3] Konishi K 2004 Phys. Rev. E 70 066201
[4] Konishi K, Senda K, Kokame H 2008 Phys. Rev. E 78 056216
[5] Prasad A, Dhamala M, Adhikari B M, Ramaswamy R 2010 Phys. Rev. E 81 027201
[6] Zhu Y, Qian X L, Yang J Z 2008 Europhys. Lett. 82 40001
[7] 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 物理学报 62 130504]
[8] 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 物理学报 62 140503]
[9] 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 物理学报 56 6815]
[10] Deng W H, Li C P 2005 Physica A 353 61
[11] 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 物理学报 57 1416]
[12] Podlubny I 1999 Fractional Differential aligns 198 (San Diego: Academic Press) p78
[13] Deng W H, Li C P, L J H 2007 Nonlinear Dyn. 48 409
[14] Zhang R X, Yang S P 2011 Chin. Phys. B 20 110506
[15] Li C P, Peng G J 2004 Chaos, Solitons and Fractals 22 443
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[1] Matthews P C, Strogatz S H 1990 Phys. Rev. Lett. 65 1701
[2] Ramana Reddy D V, Sen A, Johnston G L 1998 Phys. Rev. Lett. 80 5109
[3] Konishi K 2004 Phys. Rev. E 70 066201
[4] Konishi K, Senda K, Kokame H 2008 Phys. Rev. E 78 056216
[5] Prasad A, Dhamala M, Adhikari B M, Ramaswamy R 2010 Phys. Rev. E 81 027201
[6] Zhu Y, Qian X L, Yang J Z 2008 Europhys. Lett. 82 40001
[7] 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 物理学报 62 130504]
[8] 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 物理学报 62 140503]
[9] 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 物理学报 56 6815]
[10] Deng W H, Li C P 2005 Physica A 353 61
[11] 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 物理学报 57 1416]
[12] Podlubny I 1999 Fractional Differential aligns 198 (San Diego: Academic Press) p78
[13] Deng W H, Li C P, L J H 2007 Nonlinear Dyn. 48 409
[14] Zhang R X, Yang S P 2011 Chin. Phys. B 20 110506
[15] Li C P, Peng G J 2004 Chaos, Solitons and Fractals 22 443
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