AUTHORS: Changjin Xu, Maoxin Liao

Download as PDF

ABSTRACT: In this paper, a recharge-discharge oscillator model for the EI Ni˜no and southern oscillation with different delays is investigated. The conditions which ensure the local stability and the existence of Hopf bifurcation at the zero equilibrium of the model are obtained. It shows that the two different time delays have different effect on the dynamical behavior of the model. An example together with its numerical simulations shows the feasibility of the main results. Finally, main conclusions are included.

KEYWORDS: EI Nino and southern oscillation model, Hopf bifurcation, Stability, Periodic solution, Delay

REFERENCES:

[1] C.Z. Wang, A Unified Oscillator Model for the El Nin˜o-Southern Oscillation, J. Climate 14, 2001, pp. 98–115.

[2] J.Q. Mo, and W.T. Lin, Homotopy perturbation method of equatorial eastern Pacific for the El Nin˜o-Southern Oscillation mechanism, Chinese Phys. 14, 2005, pp. 875–878.

[3] F. Biondi, A. Gershunov, and D.R. Cayan, North Pacific Decadal Climate Variability since 1661, J. Climate 14, 2001, pp. 5–10.

[4] Y. Kushnir, W.A. Robinson, I. Blade´, N.M.J. Hall, S. Peng, and R. Sutton, Atmospheric GCM Response to Extratropical SST Anomalies: Synthesis and Evaluation, J. Climate 15, 2002, pp. 2233–2256.

[5] J.P. Chao, ENSO Dynamics, Beijing: China Meleorological Press, 1993.

[6] F.F. Jin, and W.J. Dong, Dynamic behavior and unstable state evolution of ocean-aumosphere oscillator, Acta Meteorol. Sin. 63, 2005, pp. 864– 873.

[7] F.F. Jin, An equatorial ocean recharge paradigm for ENSO. Part I: conceptual model, J. Atmos. Sci. 54, 1997, pp. 811–829.

[8] F.F. Jin, An equatorial ocean Recharge paradigm for ENSO. Part II: a stripped-down coupled model, J. Atmos. Sci. 54, 1997, pp. 830–847.

[9] J.Q. MO, W.T. Lin, and H. Wang, A class of homotopic solving method for ENSO model, Acta Math. Sci. 29, 2009, pp. 101–110.

[10] A.V. Fedorov, and S.G. Philander, A stability analysis of tropical ocean-atmosphere interactions: bridging measurements and theory for El Nin˜o. J. Climate 14, 2001, pp. 3086–3101.

[11] J.Q. MO, and W.T. Lin, Perturbed solution for the ENSO nonlinear model, Acta Phys. Sin. 53, 2004, pp. 996–998.

[12] M. Zhu, W.T. Lin, and J.Q. MO, Perturbed solution for a class of ENSO delayed sea-air oscillator, Acta Phys. Sin. 60, 2011, 030204.

[13] J.Q. MO, H. Wang, and W.T. Lin, A delayed seaair oscillator coupling model for the ENSO, Acta Phys. Sin. 55, 2006, pp. 3229–3232.

[14] G.L. Feng, W.J. Dong, X.J. Jia, and H.X. Cao, On the dynamical behavour and instability evolution of air-sea oscillator, Acta Phys. Sin. 51, 2002, pp. 1181–1185.

[15] Q. Zhao, S.K. Liu, and S.D. Liu, On the recharge-discharge oscillator model for El NinoSouthern Oscillation (ENSO), Acta Phys. Sin., 2012, 61(22): 220201.

[16] J.D. Neelin, D.S. Battisti, A.C. Hirst, F.F. Jin, Y. Wakata, T. Yamagata, and S. Zebiak, ENSO Theory, J. Geophys. Res. 103, 1998, pp. 261– 290.

[17] X.Q. Cao, J.Q. Song, W.M. Zhang, J. Zhao, and X.Q. Zhu, The modified variational iteration method for air-sea coupled dynamical system, Acta Phys. Sin. 61, 2012, 030203.

[18] W. Wang, Y. Xu, and S.P. Lu, The periodic solutions of a delayed sea-air oscillator coupling model for the ENSO, Acta Phys. Sin. 60, 2011, pp. 1–4.

[19] C.J. Xu, Bifurcation analysis for a delayed seaair oscillator coupling model for the ENSO, Acta Phys. Sin. 61, 2012, 220203.

[20] X.J. Li, X.Q. Chen, and J. Yan, Hopf bifurcation and the problem of periodic solutions in a recharge-discharge oscillator model for El Nino and southern oscillation with time delay, Acta Phys. Sin. 62, 2013, 160202.

[21] J. Cao, and M. Xiao, Stability and Hopf bifurcation in a simplified BAM neural network with two time delays, IEEE Trans. Neural Netw. 18, 2007, pp. 416–430.

[22] Z. Ge, and J. Yan, Hopf bifurcation of a predatorprey system with stage structure and harvesting, Nonlinear Anal.: TMA 74, 2011, pp. 652–660.

[23] J. Hale, Theory of Functional Differential Equations, Vol.3, Springer, Berlin, Germany, 2nd edition, 1977.

[24] H.J. Hu, and L.H. Huang, Stability and Hopf bifurcation analysis on a ring of four neurons with delays, Appl. Math. Comput. 215, 2009, pp. 889–900.

[25] Y. Kuang, Dealy Differential Equations with Applications in Populations Dynamics, Boston, USA, 1993.