Phase Synchronization Between Nonlinearly Coupled RL ssler Systems
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摘要: 讨论了具有1∶1和1∶2内共振非线性耦合系统的混沌相位同步.通过引入混沌运动的相位定义说明对于不同的内共振系统,在相对小的参数下两个子系统的平均频率差接近于0,即在弱相互作用下两个振子相位同步.随着耦合力的增加,平均频率差有波动,与1∶2内共振情形相比,在主共振条件下两个子系统平均频率差的波动较小,即使在弱作用下也是如此.线性耦合力的增加增强了相位同步效应,而非线性耦合力的增加使得两个子系统由相位同步向不同步转化,且相位动力学与Liapunov的变化有关,这也可以通过扩散云图来证实.
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关键词:
- 相位同步 /
- Rssler振子 /
- 非线性耦合 /
- Liapunov指数
Abstract: Phase synchronization between nonlinearly coupled systems with 1:1 and 1:2 resonances is investigated. By introducing the conception of phase for a chaotic motion, it demonstrates that for the different internal resonances, with relatively small parameter epsilon, both differences between the mean frequencies of the two sub-oscillators approach zero, implying phase synchronization can be achieved for weak interaction between the two oscillators. With the increase of the coupling strength, fluctuations of the frequency difference can be observed, and for the primary resonance, the amplitudes of the fluctuations of the difference seem much smaller compared with the case with frequency ratio 1:2, even with weak coupling strength. Unlike the enhance effect on the synchronization for linear coupling, the increase of nonlinear coupling strength results in the transition from phase synchronization to non-synchronized state. Further investigation reveals that the states from phase synchronization to non-synchronization are related to the critical changes of the Liapunov exponents, which can also be explained by the diffuse clouds.-
Key words:
- phase synchronization /
- R? ssler oscillator /
- nonlinearly coupled /
- Liapunov exponent
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[1] Pecora L M, Caroll T L.Synchronization in chaotic systems[J].Physical Review Letter,1990,64(8):821-824. doi: 10.1103/PhysRevLett.64.821 [2] Zhang S H, Shen K.Generalized synchronization of chaos in erbium-doped dual-ring lasers[J].Chinese Physics,2002,11(9): 894-899. doi: 10.1088/1009-1963/11/9/308 [3] Zhi L, Si S J. Global synchronization of Chua’s chaotic delay network by using linear matrix inequality[J].Chinese Physics,2004,13(8):1221-1225. doi: 10.1088/1009-1963/13/8/007 [4] Kiss I Z, Zhai Y M, Hudson J L. Collective dynamics of chaotic chemical oscillators and law of large numbers[J].Physical Review Letter,2002,88(23):238301. doi: 10.1103/PhysRevLett.88.238301 [5] Shi X, Lu Q S. Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons[J].Chinese Physics,2005,14(1):77-85. doi: 10.1088/1009-1963/14/1/016 [6] Wang J, Deng B, Tsang K M. Chaotic synchronization of neurons coupled with gap junction under external electrical stimulation[J].Chaos, Soliton & Fractals,2004,22(2):469-476. [7] Shuai J W, Durand D M. Phase synchronization in two coupled chaotic neurons[J].Physics Letters A,1999,264(4):289-297. doi: 10.1016/S0375-9601(99)00816-6 [8] Samuel B. Stability analysis for the synchronization of chaotic systems with different order: application to secure communication[J].Physics Letters A,2004,326(1):102-113. doi: 10.1016/j.physleta.2004.04.004 [9] Kim C M, Kye W H, Rim S,et al.Communication key using delay times in time-delayed chaos synchronization[J].Physics Letters A,2004,333(3/4):235-240. doi: 10.1016/j.physleta.2004.09.080 [10] Gonzalez-Miranda J M. Communications by synchronization of spatially symmetric chaotic systems[J].Physics Letters A,1999,251(2):115-120. doi: 10.1016/S0375-9601(98)00889-5 [11] Rulkov N F, Sushchik M M, Tsimring L S,et al.Generalized synchronization of chaos in directionally coupled chaotic systems[J].Physical Review E,1995,51(2): 980-994. doi: 10.1103/PhysRevE.51.980 [12] Winterhalder M, Schelter B, Kurths J,et al.Sensitivity and specificity of coherence and phase synchronization analysis[J].Physics Letters A,2006,356(1):26-34. doi: 10.1016/j.physleta.2006.03.018 [13] Li X. Phase synchronization in complex networks with decayed long-range interactions[J].Physica D: Nonlinear Phenomena,2006,223(2):242-247. doi: 10.1016/j.physd.2006.09.026 [14] Alatriste F R, Mateos J L. Phase synchronization in tilted deterministic ratchets[J].Physica A: Statistical Mechanics and Its Applications,2006,372(2):263-271. doi: 10.1016/j.physa.2006.08.038 [15] Gabor D. Theory of communication[J].J IEE (London),Part Ⅲ,1946,93(26):429-457. [16] Pikovsky A, Roseblum M G, Osipov G,et al. Phase synronization of chaotic oscillators by external driving[J].Physica D,1997,104(3):219-238. doi: 10.1016/S0167-2789(96)00301-6 [17] Pikovsky A. Phase synronization of chaotic oscillators by a periodic external field[J].Journal of Communications Technology Electronics,1985,30(3):1970-1974. [18] Pikovsky A, Roseblum M G, Osipov G,et al.Phase synronization in regular and chaotic systems[J].Journal of Bifurcation and Chaos,2000,10(10):2291-2305. [19] Landa P S, Roseblum M G. Synchronization and chaotization of oscillations in coupled self-oscillating systems[J].Application Mechanics Review,1993,46(7):414-426. doi: 10.1115/1.3120370 [20] Zhang Z G, Hu G.Generalized synchronization versus phase synchronization[J].Physical Review E,2000,62(6):7882-7885. doi: 10.1103/PhysRevE.62.7882 [21] Lv J H, Zhou T S, Zhang S C.Chaos synchronization between linearly coupled chaotic systems[J].Chaos, Solitons & Fractals,2002,14(4):529-541. [22] Landa P S, Perminov S M.Synchronization of the chaotic oscillations in the Mackey-Glass system[J].Radiofizika,1987,30(3):437-439. [23] Coombes S. Phase locking in the networks of synaptically coupled McKean relaxation oscillators[J].Physica D,2001,160(3):173-188. doi: 10.1016/S0167-2789(01)00352-9 [24] Palus M. Detecting phase synchronization in noisy systems[J].Physics Letters A,1997,235(4):341-351. doi: 10.1016/S0375-9601(97)00635-X [25] Bi Q. Bifurcation of traveling wave solutions from KdV equation to Camassa-Holm equation[J].Physics Letters A,2005,344(5):361-368. doi: 10.1016/j.physleta.2005.06.096 [26] Bi Q. Dynamical analysis of two coupled parametrically excited Van del Pol oscillators[J].Journal of Non-Linear Mechanics,2004,39(1) :33-54. doi: 10.1016/S0020-7462(02)00126-9 [27] Bi Q. Dynamics and modulated chaos of coupled oscillators[J].Journal of Bifurcation and Chaos,2004,14(1):337-346. doi: 10.1142/S0218127404009041
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