Periodic Solutions to the Stochastic-Dynamic Climate Model With Sea-Air Interaction

CHEN Li-juan; LU Shi-ping; XU Jing

doi:10.3879/j.issn.1000-0887.2015.10.008

Volume 36 Issue 10

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(10): 1085-1094

CHEN Li-juan, LU Shi-ping, XU Jing. Periodic Solutions to the Stochastic-Dynamic Climate Model With Sea-Air Interaction[J]. Applied Mathematics and Mechanics, 2015, 36(10): 1085-1094. doi: 10.3879/j.issn.1000-0887.2015.10.008

Citation:

PDF( 352 KB)

Periodic Solutions to the Stochastic-Dynamic Climate Model With Sea-Air Interaction

doi: 10.3879/j.issn.1000-0887.2015.10.008

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P.R.China

Funds: The National Natural Science Foundation of China(11271197)

Received Date: 2015-05-06
Rev Recd Date: 2015-07-13
Publish Date: 2015-10-15

Abstract

Abstract

Usually, most of the stochastic-dynamic climate models were addressed under the assumption that the stochastic forcing terms were white noises. However, many fast climate variables are expressed as nonlinear stochastic processes other than white noises. The stochastic forcing terms in the sea-air interaction model were improved, and a reasonable model was built accordingly. The Mawhin’s continuation theorem as a very effective and general method to study the existence of periodic solutions to dynamic systems, was applied to the problem of periodic solutions to the proposed stochastic-dynamic climate model with sea-air interaction, in which the stochastic forcing terms were some stochastic processes differring from white noises. The existence of periodic solutions to the model under certain conditions was proved, and the potential application value of the results was discussed.
- sea-air interaction,
- stochastic-dynamic climate system,
- periodic solution

FullText(HTML)

References(17)

References

[1]	Hasselman K. Stochastic climate models, part Ⅰ: theory[J]. Tellus,1976,28（6）: 473-486.
[2]	Frankignoul C, Hasselman K. Stochastic climate models, part II: application to sea-surface temperature anomalies and thermocline variability[J]. Tellus,1977,29(4): 289-305.
[3]	Lemke P. Stochastic perturbation of deterministic systems, part 3: application to zonally averaged energy models[J]. Tellus,1977,29(5): 385-392.
[4]	李麦村. 海气相互作用的随机-动力理论[J]. 海洋学报, 1981,3(3): 382-389.(LI Mai-cun. The stochastic theory of air-sea interaction[J]. Acta Oceanologica Sinica,1981,3(3): 382-389.(in Chinese))
[5]	Mller J D, Shapiro L J. Influences of asymmetric heating on hurricane evolution in the MM5[J]. Journal of the Atmospheric Sciences,2005,62(11): 3974-3992.
[6]	Luo J J, Masson S, Behera S, Yamagata T. Extended ENSO predictions using a fully coupled ocean-atmosphere model[J]. Journal of Climate,2008,21(1): 84-93.
[7]	FENG Guo-ling, CAO Yong-zhong, CAO Hong-xing. Air-sea stochastic climatic model and its application[J]. Chinese Journal of Computational Physics, 2001,18（1）: 57-63.
[8]	Zhang R H, Zebiak S E. An embedding method for improving interannual variability simulations in a hybrid coupled model of the tropical Pacific Ocean-atmosphere system[J]. Journal of Climate,2004,17(14): 2794-2812.
[9]	李麦村, 黄嘉佑. 关于海温准三年及半年周期振荡的随机气候模式[J]. 气象学报, 1984,42(2): 168-176.(LI Mai-cun, HUANG Jia-you. A stochastic climate model on the quasithree-yearly and half-yearly oscillation of the sea surface temperature[J]. Journal of Meteorology,1984,42(2): 168-176.(in Chinese))
[10]	WANG Chun-zai. A unified oscillator model for the El Nino-southern oscillation[J]. Journal of Climate,2001,14（1）: 98-115.
[11]	LI Xiao-jing. The periodic solution to the model for the El Nino-southern oscillation[J]. Chinese Physics B,2010,19（3）: 030201-1-030201-3.
[12]	DU Zeng-ji, LIN Wan-tao, MO Jia-qi. Perturbation method of studying the El Nino oscillation with two parameters by using the delay sea-air oscillator model[J]. Chinese Physics B,2012,21(9): 090201-1-090201-5.
[13]	陈丽娟, 鲁世平. 一类太空等离子体单粒子运动模型的同宿轨[J]. 应用数学和力学, 2013,34(12): 1258-1265.(CHEN Li-juan, LU Shi-ping. Homoclinic orbit of the motion model for a single space plasma particle[J]. Applied Mathematics and Mechanics,2013,34(12): 1258-1265.(in Chinese))
[14]	陈丽娟, 鲁世平. 零维气候系统非线性模式的周期解问题[J]. 物理学报, 2013,62(20): 200201-1-200201-4.(CHEN Li-juan, LU Shi-ping. The problem of periodic solution of nonlinear model in zero-dimensional climate system[J]. Acta Physica Sinica,2013,62(20): 200201-1-200201-4.(in Chinese))
[15]	陈丽娟, 鲁世平. 无晨昏电场下带电粒子在中性片磁场中运动的周期轨[J]. 应用数学和力学, 2014,35(11): 1280-1286.(CHEN Li-juan, LU Shi-ping. The periodic orbits of electric particles sporting in neutral sheet magnetic field without the dawn-dusk electric field[J]. Applied Mathematics and Mechanics,2014,35(11): 1280-1286.(in Chinese))
[16]	Gaines R E, Mawhin J L. Coincidence Degree and Nonlinear Differential Equations [M]. Berlin: Springer, 1977.
[17]	LU Shi-ping, CHEN Li-juan. The problem of existence of periodic solutions for neutral functional differential system with nonlinear difference operator[J]. J Math Anal Appl,2012,387(2): 1127-1136.