Taming of the Hopf bifurcation in a driven El Niño model-Reference-Cited by-同舟云学术

Taming of the Hopf bifurcation in a driven El Niño model

Published:2020-07-03 Issue:8 Volume:75 Page:699-704
ISSN:1865-7109
Container-title:Zeitschrift für Naturforschung A
language:en
Short-container-title:

Author:

Rajagopal Karthikeyan¹^ORCID,Premraj Durairaj²,Thamilmaran Kathamuthu²,Pham Viet-Thanh¹,Karthikeyan Anitha¹,Duraisamy Prakash³

Affiliation:

1. Nonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering , Ton Duc Thang University , Ho Chi Minh City , Vietnam

2. Centre for Nonlinear Dynamics, School of Physics , Bharathidasan University , Tiruchirappalli , India

3. Center for Nonlinear Dynamics and Control, Mekelle University , Mekelle , Ethiopia

Abstract

Abstract In this paper, we consider the well-known Vallis model for El Niño driven by an external excitation. The bifurcation studies on the driven Vallis model are conducted with different control parameters. Then we discuss about the taming of the Hopf bifurcation by varying the driving function. We could note that the system changes its state from stable steady state to oscillatory state and vice versa which is achieved by changing the driving function. Finally, two parameter bifurcation plots are derived to show that impact of the driving function on the system bifurcation points.

Funder

Center for Nonlinear Dynamics, Defence University, Ethiopia

Publisher

Walter de Gruyter GmbH

Subject

Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics

Link

https://www.degruyter.com/document/doi/10.1515/zna-2020-0082/pdf

Reference24 articles.

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3. A. P. Krishchenko, K. E. Starkov, “Localization of compact invariant compact sets of nonlinear time-varying systems,” Int. J. Bifurcat. Chaos., vol. 18, pp. 1599–1604, 2008. https://doi.org/10.1142/s021812740802121x.

4. R. D. Euzébio, J. Llibre, “Periodic solutions of El Niño model through the vallis differential system,” Discret. Contin. Dyn. S., vol. 34, pp. 3455–3469, 2014. https://doi.org/10.3934/dcds.2014.34.3455.

5. B. M. Garay, B. Indig, “Chaos in vallis asymmetric lorenz model for el niño,” Chaos. Solitons. Fractals., vol. 75, pp. 253–62, 2015, https://doi.org/10.1016/j.chaos.2015.02.015.

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