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Periodic solutions of El Niño model through the Vallis differential system

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  • By rescaling the variables, the parameters and the periodic function of the Vallis differential system we provide sufficient conditions for the existence of periodic solutions and we also characterize their kind of stability. The results are obtained using averaging theory.
    Mathematics Subject Classification: Primary: 86A10, 37C60, 34C07.


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  • [1]

    A. Buică, J. P. Françoise and J. Llibre, Periodic solutions of nonlinear periodic differential systems with a small parameter, Comm. on Pure and Appl. Anal., 6 (2007), 103-111.doi: 10.3934/cpaa.2007.6.103.


    J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Revised and Corrected Reprint of the 1983 Original, Applied Mathematical Sciences, 42, Springer-Verlag, New York, 1990.


    A. Kanatnikov and A. Krishchenko, Localization of invariant compact sets of nonautonomous systems, Differ. Equ., 45 (2009), 46-52.doi: 10.1134/S0012266109010054.


    A. P. Krishchenko and K. E. Starkov, Localization of compact invariant sets of nonlinear time-varying systems, Intern. Journal of Bifurcation and Chaos, 18 (2008), 1599-1604.doi: 10.1142/S021812740802121X.


    J. Llibre and C. Vidal, Periodic solutions of a periodic FitzHugh-Nagumo differential system, to appear.


    I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations, (Russian) Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956.


    M. Roseau, Vibrations Non Linéaires et Théorie de la Stabilité, (French) Springer Tracts in Natural Philosophy, Vol. 8 Springer-Verlag, Berlin-New York, 1966.


    J. A. Sanders, F. Verhulst and J. Murdock, Averaging Method in Nonlinear Dynamical Systems, Applied Mathematical Sciences, 59. Springer, New York, 2007. xxii+431 pp.


    D. Strozzi, On the Origin of Interannual and Irregular Behaviour in the El Niño Properties, Report of Department of Physics, Princeton University, available at the WEB, 1999.


    G. K. Vallis, Conceptual models of El Niño and the southern oscillation, Geophys. Res., 93 (1988), 13979-13991.doi: 10.1029/JC093iC11p13979.

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