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In this paper, a recharge-discharge oscillator model for El Niño and southern oscillation with time delay is investigated. We obtain the critical time delay associated with Hopf bifurcation, and discuss the problem of periodic solutions for the model by using Maehin’s continuation theorem.
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Keywords:
- time delay /
- El Niñ /
- o and southern oscillation model /
- Hopf bifurcation
[1] Feng G L, Dong W J, Jia X J 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静 2002 51 1181]
[2] Feng G L, Dong W J 2005 Acta Meteo. Sin. 63 864 (in Chinese) [封国林, 董文杰 2005 气象学报 63 864]
[3] Liu S S, Fu Z T, Liu S D 2002 Acta Phys. Sin. 51 10 (in Chinese) [刘式适, 傅遵涛, 刘式达 2002 51 10]
[4] Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 1221 (in Chinese) [张家树, 肖先赐 2000 49 1221]
[5] Jin F F 1997 J. Atmos. Sci. 54 811
[6] Jin F F 1997 J. Atmos. Sci. 54 830
[7] Wang B, Feng Z 1999 J. Atmos. Sci. 56 5
[8] Wang C Z 2001 J. Climate 14 98
[9] Mo J Q, Lin W T, Zhu J 2006 Adv. Math. 35 232
[10] Mo J Q, Lin W T, Wang H 2009 Acta Math. Sci. 29 101
[11] Li X J 2010 Chin. Phys. B 19 030201
[12] Cao X Q, Song J Q, Zhang W M, Zhao J, Zhu X Q 2012 Acta Phys. Sin. 61 030203 (in Chinese) [曹小群, 宋君强, 张卫民, 赵军, 朱小谦 2012 61 030203]
[13] Zhao Q, Liu S S, Liu S D 2012 Acta Phys. Sin. 61 220201 (in Chinese) [赵强, 刘式适, 刘式达 2012 61 220201]
[14] Li X J 2007 Chin. Phys. 16 2837
[15] Li X J 2008 Chin. Phys. B 17 1946
[16] Li X J 2008 Acta Phys. Sin. 57 5366 (in Chinese) [李晓静 2008 57 5366)
[17] Li X J 2010 Chin. Phys. B 19 020202
[18] Li X J, Chen X Q 2012 Acta Phys. Sin. 61 210201 (in Chinese) [李晓静, 陈绚青 2012 61 210201]
[19] Li X J, Chen X Q, Yan J 2013 Acta Phys. Sin. 62 090202 (in Chinese) [李晓静, 陈绚青, 严静 2013 62 090202]
[20] Hale J, Lunel S V 1993 Introduction to Functional Differential Equations (New York: Springer-Verlag)
[21] Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[22] Tang X H, Li X 2009 Nonlinear Anal. 71 1140
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[1] Feng G L, Dong W J, Jia X J 2002 Acta Phys. Sin. 51 1181 (in Chinese) [封国林, 董文杰, 贾晓静 2002 51 1181]
[2] Feng G L, Dong W J 2005 Acta Meteo. Sin. 63 864 (in Chinese) [封国林, 董文杰 2005 气象学报 63 864]
[3] Liu S S, Fu Z T, Liu S D 2002 Acta Phys. Sin. 51 10 (in Chinese) [刘式适, 傅遵涛, 刘式达 2002 51 10]
[4] Zhang J S, Xiao X C 2000 Acta Phys. Sin. 49 1221 (in Chinese) [张家树, 肖先赐 2000 49 1221]
[5] Jin F F 1997 J. Atmos. Sci. 54 811
[6] Jin F F 1997 J. Atmos. Sci. 54 830
[7] Wang B, Feng Z 1999 J. Atmos. Sci. 56 5
[8] Wang C Z 2001 J. Climate 14 98
[9] Mo J Q, Lin W T, Zhu J 2006 Adv. Math. 35 232
[10] Mo J Q, Lin W T, Wang H 2009 Acta Math. Sci. 29 101
[11] Li X J 2010 Chin. Phys. B 19 030201
[12] Cao X Q, Song J Q, Zhang W M, Zhao J, Zhu X Q 2012 Acta Phys. Sin. 61 030203 (in Chinese) [曹小群, 宋君强, 张卫民, 赵军, 朱小谦 2012 61 030203]
[13] Zhao Q, Liu S S, Liu S D 2012 Acta Phys. Sin. 61 220201 (in Chinese) [赵强, 刘式适, 刘式达 2012 61 220201]
[14] Li X J 2007 Chin. Phys. 16 2837
[15] Li X J 2008 Chin. Phys. B 17 1946
[16] Li X J 2008 Acta Phys. Sin. 57 5366 (in Chinese) [李晓静 2008 57 5366)
[17] Li X J 2010 Chin. Phys. B 19 020202
[18] Li X J, Chen X Q 2012 Acta Phys. Sin. 61 210201 (in Chinese) [李晓静, 陈绚青 2012 61 210201]
[19] Li X J, Chen X Q, Yan J 2013 Acta Phys. Sin. 62 090202 (in Chinese) [李晓静, 陈绚青, 严静 2013 62 090202]
[20] Hale J, Lunel S V 1993 Introduction to Functional Differential Equations (New York: Springer-Verlag)
[21] Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[22] Tang X H, Li X 2009 Nonlinear Anal. 71 1140
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