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A class of asymptotic solution of sea-air time delay oscillator for the El Niño-southern oscillation mechanism

Ouyang Cheng Lin Wan-Tao Cheng Rong-Jun Mo Jia-Qi

A class of asymptotic solution of sea-air time delay oscillator for the El Niño-southern oscillation mechanism

Ouyang Cheng, Lin Wan-Tao, Cheng Rong-Jun, Mo Jia-Qi
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  • A class of coupled system of the El Niño-southern oscillation mechanism is studied. Using the singular perturbation theory and method, the outer solution and the initial layer corrective term of the model are solved. And then, the asymptotic expansion of the solution for the problem is obtained and the asymptotic behavior of solution is considered.
    • Funds: Project supported by the National Basic Research Program of China (Grant No. 2011CB403501), the National Natural Science Foundation of China (Grant Nos. 41275062, 41175058, 11202106), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110502) and the Natural Science Foundation from the Education Bureau of Anhui Province, China (Grant Nos. KJ2012A001, KJ2012Z245).
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    [2]

    Wang C, Weisberg R H 1996 J. Climate 9 3132

    [3]

    Wang C 2001 J. Climath 14 98

    [4]

    Wang C 2001 Adv. Atmos. Sci. 18 674

    [5]

    Zhou T J, Yu R, Li H, Wang B 2008 J. Climate 21 3833

    [6]

    Zhou T J, Wu B, Wang B 2009 J. Climate 22 1159

    [7]

    Zhou T J, Zou L 2010 J. Climate 23 6009

    [8]

    Zhou T J, Zhang J 2011 J. Climate 24 1053

    [9]

    Cabanes C, Huck T, De Verderce A G 2006 J. Phys. Oceanogyr. 36 1739

    [10]

    Qiu B, Chen S M 2006 J. Phys. Oceanogyr. 36 1751

    [11]

    Zhang Y C, Lu K C, Zhang M 2011 Sci. Meteorodogica Sin. 31 11 (in Chinese) [张永垂, 路凯程, 张 铭 2011 气象科学 31 11]

    [12]

    Lu K C, Zhang Y C, Zhang M 2011 Sci. Meteorodogica Sin. 31 17 (in Chinese) [路凯程, 张永垂, 张 铭 2011 气象科学 31 17]

    [13]

    Zhang Y C, Lu K C, Zhang M 2012 Clinmatic and Environmental Research 17 217 (in Chinese) [张永垂, 路凯程, 张铭 2012 气候与环境研究 17 217]

    [14]

    Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)

    [15]

    Ramos M 2009 J. Math. Anal. Appl. 352 246

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    D'Aprile T, Pistoia A 2010 J. Diff. Eqs. 248 556

    [17]

    Faye L, Frenod E, Seck D 2011 Discrete Contin. Dyn. Sys. 29 1001

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    Mo J Q 2009 Sci. China G 39 568

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    Mo J Q 2009 Chin. Phys. Lett. 26 060202

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    Mo J Q 2009 Chin. Phys. Lett. 26 010204

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    Mo J Q, Lin Y H, Lin W T 2010 Acta Phys. Sin. 59 6701 (in Chinese) [莫嘉琪, 林一骅, 林万涛 2010 物理学报 59 6701]

    [22]

    Mo J Q 2011 Acta Phys. Sin. 60 090203 (in Chinese) [莫嘉琪 2011 物理学报 60 090203]

    [23]

    Mo J Q 2010 Commun. Theor. Phys. 53 440

    [24]

    Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205

  • [1]

    Xue Y, Cane M A, Zebiak S E 1997 Monthly Weather Rev. 125 2043

    [2]

    Wang C, Weisberg R H 1996 J. Climate 9 3132

    [3]

    Wang C 2001 J. Climath 14 98

    [4]

    Wang C 2001 Adv. Atmos. Sci. 18 674

    [5]

    Zhou T J, Yu R, Li H, Wang B 2008 J. Climate 21 3833

    [6]

    Zhou T J, Wu B, Wang B 2009 J. Climate 22 1159

    [7]

    Zhou T J, Zou L 2010 J. Climate 23 6009

    [8]

    Zhou T J, Zhang J 2011 J. Climate 24 1053

    [9]

    Cabanes C, Huck T, De Verderce A G 2006 J. Phys. Oceanogyr. 36 1739

    [10]

    Qiu B, Chen S M 2006 J. Phys. Oceanogyr. 36 1751

    [11]

    Zhang Y C, Lu K C, Zhang M 2011 Sci. Meteorodogica Sin. 31 11 (in Chinese) [张永垂, 路凯程, 张 铭 2011 气象科学 31 11]

    [12]

    Lu K C, Zhang Y C, Zhang M 2011 Sci. Meteorodogica Sin. 31 17 (in Chinese) [路凯程, 张永垂, 张 铭 2011 气象科学 31 17]

    [13]

    Zhang Y C, Lu K C, Zhang M 2012 Clinmatic and Environmental Research 17 217 (in Chinese) [张永垂, 路凯程, 张铭 2012 气候与环境研究 17 217]

    [14]

    Barbu L, Morosanu G 2007 Singularly Perturbed Boundary-Value Problems (Basel: Birkhauserm Verlag AG)

    [15]

    Ramos M 2009 J. Math. Anal. Appl. 352 246

    [16]

    D'Aprile T, Pistoia A 2010 J. Diff. Eqs. 248 556

    [17]

    Faye L, Frenod E, Seck D 2011 Discrete Contin. Dyn. Sys. 29 1001

    [18]

    Mo J Q 2009 Sci. China G 39 568

    [19]

    Mo J Q 2009 Chin. Phys. Lett. 26 060202

    [20]

    Mo J Q 2009 Chin. Phys. Lett. 26 010204

    [21]

    Mo J Q, Lin Y H, Lin W T 2010 Acta Phys. Sin. 59 6701 (in Chinese) [莫嘉琪, 林一骅, 林万涛 2010 物理学报 59 6701]

    [22]

    Mo J Q 2011 Acta Phys. Sin. 60 090203 (in Chinese) [莫嘉琪 2011 物理学报 60 090203]

    [23]

    Mo J Q 2010 Commun. Theor. Phys. 53 440

    [24]

    Mo J Q, Lin W T, Lin Y H 2011 Chin. Phys. B 20 070205

  • [1] Lin Yi-Hua, Lin Wan-Tao, Mo Jia-Qi. Approximate solution of sea-air oscillator for El Ni?o-southern oscillation model. Acta Physica Sinica, 2010, 59(10): 6707-6711. doi: 10.7498/aps.59.6707
    [2] SHI Lan-Fang, Ouyang Cheng, Mo Jia-Qi. The asymptotic solving methodof traveling wave solution to a class of sea-air coupled oscillator model. Acta Physica Sinica, 2012, 61(12): 120201. doi: 10.7498/aps.61.120201
    [3] Mo Jia-Qi, Lin Wan-Tao, Wang Hui. Perturbative solution for a class of El Ni?o sea-air oscillator mechanism. Acta Physica Sinica, 2005, 54(9): 3967-3970. doi: 10.7498/aps.54.3967
    [4] Li Xiao-Jing, Chen Xuan-Qing, Yan Jing. Hopf bifurcation and the problem of periodic solutions in a recharge-discharge oscillator model for El Niño and southern oscillation with time delay. Acta Physica Sinica, 2013, 62(16): 160202. doi: 10.7498/aps.62.160202
    [5] Xie Feng, Mo Jia-Qi, Lin Yi-Hua, Lin Wan-Tao. The solutions for disturbed El Ni o/La Ni a-southern oscillation model. Acta Physica Sinica, 2011, 60(1): 010201. doi: 10.7498/aps.60.010201
    [6] Mo Jia-Qi, Lin Wan-Tao. Perturbed solution for the ENSO nonlinear model. Acta Physica Sinica, 2004, 53(4): 996-998. doi: 10.7498/aps.53.996
    [7] Wang Wen, Xu Yan, Lu Shi-Ping. The periodic solutions of a delayed sea-air oscillator coupling model for the ENSO. Acta Physica Sinica, 2011, 60(3): 030205. doi: 10.7498/aps.60.030205
    [8] Mo Jia-Qi, Lin Yi-Hua, Lin Wan-Tao. Approximate solution to a nonlinear oscillation of global climate model. Acta Physica Sinica, 2009, 58(10): 6692-6695. doi: 10.7498/aps.58.6692
    [9] Mo Jia-Qi, Lin Wan-Tao, Lin Yi-Hua. Asymptotic solution to the delay sea-sir oscillator for El Nio/La Nia-southern oscillation mechnism. Acta Physica Sinica, 2011, 60(8): 080202. doi: 10.7498/aps.60.080202
    [10] Han Xiang-Lin, Du Zeng-Ji, Mo Jia-Qi. Singular perturbation solution of a class of sea-air oscillator for the El Niño/La Niña-southern oscillation. Acta Physica Sinica, 2012, 61(20): 200208. doi: 10.7498/aps.61.200208
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  • Received Date:  20 October 2012
  • Accepted Date:  01 November 2012
  • Published Online:  20 March 2013

A class of asymptotic solution of sea-air time delay oscillator for the El Niño-southern oscillation mechanism

  • 1. Faculty of Science, Huzhou Teachers College, Huzhou 313000, China;
  • 2. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China;
  • 3. Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
  • 4. Department of Mathematics, Anhui Normal University, Wuhu 241003, China
Fund Project:  Project supported by the National Basic Research Program of China (Grant No. 2011CB403501), the National Natural Science Foundation of China (Grant Nos. 41275062, 41175058, 11202106), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110502) and the Natural Science Foundation from the Education Bureau of Anhui Province, China (Grant Nos. KJ2012A001, KJ2012Z245).

Abstract: A class of coupled system of the El Niño-southern oscillation mechanism is studied. Using the singular perturbation theory and method, the outer solution and the initial layer corrective term of the model are solved. And then, the asymptotic expansion of the solution for the problem is obtained and the asymptotic behavior of solution is considered.

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