Periodic solutions of El Niño model through the Vallis differential system

Rodrigo Donizete Euzébio; Jaume Llibre

doi:10.3934/dcds.2014.34.3455

Article Contents

2014, Volume 34, Issue 9: 3455-3469. Doi: 10.3934/dcds.2014.34.3455

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Periodic solutions of El Niño model through the Vallis differential system

Rodrigo Donizete Euzébio^1, and
Jaume Llibre^2,

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
2.
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia

Received: March 31, 2013

Revised: November 30, 2013

Published: August 2014

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Abstract

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.

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Mathematics Subject Classification: Primary: 86A10, 37C60, 34C07.

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References

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