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Periodic solutions of El Niño model through the Vallis differential system
1. | Department of Mathematics, IBILCE, UNESP - Univ Estadual Paulista, Rua Cristovão Colombo, 2265, Jardim Nazareth, CEP 15.054-000, Sao José de Rio Preto, SP, Brazil |
2. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia |
References:
[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.
doi: 10.3934/cpaa.2007.6.103. |
[2] |
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, (1990).
|
[3] |
A. Kanatnikov and A. Krishchenko, Localization of invariant compact sets of nonautonomous systems,, Differ. Equ., 45 (2009), 46.
doi: 10.1134/S0012266109010054. |
[4] |
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.
doi: 10.1142/S021812740802121X. |
[5] |
J. Llibre and C. Vidal, Periodic solutions of a periodic FitzHugh-Nagumo differential system,, to appear., (). Google Scholar |
[6] |
I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations,, (Russian) Gosudarstv. Izdat. Tehn.-Teor. Lit., (1956).
|
[7] |
M. Roseau, Vibrations Non Linéaires et Théorie de la Stabilité,, (French) Springer Tracts in Natural Philosophy, (1966).
|
[8] |
J. A. Sanders, F. Verhulst and J. Murdock, Averaging Method in Nonlinear Dynamical Systems,, Applied Mathematical Sciences, (2007).
|
[9] |
D. Strozzi, On the Origin of Interannual and Irregular Behaviour in the El Niño Properties,, Report of Department of Physics, (1999). Google Scholar |
[10] |
G. K. Vallis, Conceptual models of El Niño and the southern oscillation,, Geophys. Res., 93 (1988), 13979.
doi: 10.1029/JC093iC11p13979. |
show all references
References:
[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.
doi: 10.3934/cpaa.2007.6.103. |
[2] |
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, (1990).
|
[3] |
A. Kanatnikov and A. Krishchenko, Localization of invariant compact sets of nonautonomous systems,, Differ. Equ., 45 (2009), 46.
doi: 10.1134/S0012266109010054. |
[4] |
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.
doi: 10.1142/S021812740802121X. |
[5] |
J. Llibre and C. Vidal, Periodic solutions of a periodic FitzHugh-Nagumo differential system,, to appear., (). Google Scholar |
[6] |
I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations,, (Russian) Gosudarstv. Izdat. Tehn.-Teor. Lit., (1956).
|
[7] |
M. Roseau, Vibrations Non Linéaires et Théorie de la Stabilité,, (French) Springer Tracts in Natural Philosophy, (1966).
|
[8] |
J. A. Sanders, F. Verhulst and J. Murdock, Averaging Method in Nonlinear Dynamical Systems,, Applied Mathematical Sciences, (2007).
|
[9] |
D. Strozzi, On the Origin of Interannual and Irregular Behaviour in the El Niño Properties,, Report of Department of Physics, (1999). Google Scholar |
[10] |
G. K. Vallis, Conceptual models of El Niño and the southern oscillation,, Geophys. Res., 93 (1988), 13979.
doi: 10.1029/JC093iC11p13979. |
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