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本文研究了一类太阳强迫的厄尔尼诺/南方涛动(ENSO)充电振子数理模型,通过数学变换将此ENSO振子方程组变换为有周期强迫项的van der Pol-Duffing方程,利用谐波平衡法定性分析得到此ENSO系统发生Hopf分岔的条件并做简单数值模拟,结果发现随着强迫作用增大,11年周期太阳循环强迫的ENSO系统经历准周期、倍频锁相到混沌的过程.
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关键词:
- 厄尔尼诺/南方涛动 /
- van der Pol-Duffing方程 /
- Hopf分岔 /
- 混沌
A class of solar-forced recharge oscillator model for the El Niño /Southern Oscillation (ENSO) is considered. By transforming the ENSO model equations into the van der Pol-Duffing oscillator with periodic forcing, we obtain the Hopf bifurcation conditions by the harmonic balance method. Numerical simulations also show that the 11-yr solar-cycle forced ENSO system undergoes a transition from the quasi-periodicity route to chaos as the solar-cycle forcing is increased.-
Keywords:
- El Niñ /
- o/Southern Oscillation /
- van der Pol-Duffing equation /
- Hopf bifurcation
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[2] Clarke A J 2008 An Introduction to the Dynamics of El Niño and the Southern Oscillation (London: Academic Press)
[3] Sarachik E S and Cane M A 2010 The El Niñ-Southern Oscillation Phenomenon (Cambridge: Cambridge University Press)
[4] McPhaden M J, S E Zebiak, Glantz M H 2006 Science 314 1740
[5] Lin J L 2009 Chin. Ann. Math. 30B 715
[6] Wang C Z 2001 Adv. Atmos. Sci. 18 674
[7] Zhao Q, Liu S K, Liu S D 2012 Acta Phys. Sin. 61 220201 (in Chinese) [赵强, 刘式适, 刘式达 2012 物理学报 61 220201]
[8] Li X J 2010 Chin. Phys. B 19 030201
[9] Wang W, Xu Y, Lu S P 2011 Acta Phys. Sin. 60 030205 (in Chinese) [王雯, 徐燕, 鲁世平 2011 物理学报 60 030205]
[10] Zhang W F, Zhao Q 2013 Chin. Phys. B 22 120201
[11] Zaliapin I, Ghil M 2010 Nonlin. Processes Geophys. 17 123
[12] Tziperman E, Stone L, Cane M, Jarosh H 1994 Science 264 72
[13] Tziperman E, Cane M A, Zebiak S E 1995 J. Atmos. Sci. 50 293
[14] Zhou Q, Chen W, Zhou W 2013 J. Geophys. Res.: Atmospheres 118 5111
[15] Meehl G A, Arblaster J M, Matthes K, Sassi F, Loon H 2009 Science 325 1114
[16] Roy I, Haigh J D 2010 Atmos. Chem. Phys. 10 3147
[17] Haam E, Tung K K 2012 J. Atmos. Sci. 69 2934
[18] Haam E, Tung K K 2013 J. Atmos. Sci. 70 9
[19] White W B, Liu Z 2008 Geophys. Res. Lett. 35 L19607
[20] Saltzman B 2002 Dynamical paleoclimatology: generalized theory of global climate change (international geophysics) (London: Academic Press)
[21] Rial J A, Saha R 2013 Abrupt Climate Change: Mechanisms, Patterns, and Impacts American Geophysical Union, Washington, D.C.
[22] B. De Saedeleer, Crucifix M, Wieczorek S 2013 Climate Dyn. 40 273
[23] Jin F F 1997 J. Atmos. Sci. 54 811
[24] Zhu B Z, Jin F F, Liu Z Y 1991 An Introduction to the nonlinear Dynamics of the atmosphere and ocean (Beijing: Ocean Press) (in Chinese) [朱抱真, 金飞飞, 刘征宇 1991 大气和海洋的非线性动力学概论 (北京: 海洋出版社)]
[25] Hu H Y 2000 Applied Nonlinear Dynamics (Beijing: Aviation Industry Press) (in Chinese) [胡海岩 2000 应用非线性动力学 (北京: 航空工业出版社)]
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[1] Philander, S G 1990 El Niño, La Niña, and the Southern Oscillation (London: Academic Press)
[2] Clarke A J 2008 An Introduction to the Dynamics of El Niño and the Southern Oscillation (London: Academic Press)
[3] Sarachik E S and Cane M A 2010 The El Niñ-Southern Oscillation Phenomenon (Cambridge: Cambridge University Press)
[4] McPhaden M J, S E Zebiak, Glantz M H 2006 Science 314 1740
[5] Lin J L 2009 Chin. Ann. Math. 30B 715
[6] Wang C Z 2001 Adv. Atmos. Sci. 18 674
[7] Zhao Q, Liu S K, Liu S D 2012 Acta Phys. Sin. 61 220201 (in Chinese) [赵强, 刘式适, 刘式达 2012 物理学报 61 220201]
[8] Li X J 2010 Chin. Phys. B 19 030201
[9] Wang W, Xu Y, Lu S P 2011 Acta Phys. Sin. 60 030205 (in Chinese) [王雯, 徐燕, 鲁世平 2011 物理学报 60 030205]
[10] Zhang W F, Zhao Q 2013 Chin. Phys. B 22 120201
[11] Zaliapin I, Ghil M 2010 Nonlin. Processes Geophys. 17 123
[12] Tziperman E, Stone L, Cane M, Jarosh H 1994 Science 264 72
[13] Tziperman E, Cane M A, Zebiak S E 1995 J. Atmos. Sci. 50 293
[14] Zhou Q, Chen W, Zhou W 2013 J. Geophys. Res.: Atmospheres 118 5111
[15] Meehl G A, Arblaster J M, Matthes K, Sassi F, Loon H 2009 Science 325 1114
[16] Roy I, Haigh J D 2010 Atmos. Chem. Phys. 10 3147
[17] Haam E, Tung K K 2012 J. Atmos. Sci. 69 2934
[18] Haam E, Tung K K 2013 J. Atmos. Sci. 70 9
[19] White W B, Liu Z 2008 Geophys. Res. Lett. 35 L19607
[20] Saltzman B 2002 Dynamical paleoclimatology: generalized theory of global climate change (international geophysics) (London: Academic Press)
[21] Rial J A, Saha R 2013 Abrupt Climate Change: Mechanisms, Patterns, and Impacts American Geophysical Union, Washington, D.C.
[22] B. De Saedeleer, Crucifix M, Wieczorek S 2013 Climate Dyn. 40 273
[23] Jin F F 1997 J. Atmos. Sci. 54 811
[24] Zhu B Z, Jin F F, Liu Z Y 1991 An Introduction to the nonlinear Dynamics of the atmosphere and ocean (Beijing: Ocean Press) (in Chinese) [朱抱真, 金飞飞, 刘征宇 1991 大气和海洋的非线性动力学概论 (北京: 海洋出版社)]
[25] Hu H Y 2000 Applied Nonlinear Dynamics (Beijing: Aviation Industry Press) (in Chinese) [胡海岩 2000 应用非线性动力学 (北京: 航空工业出版社)]
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