Chaos in Vallis’ asymmetric Lorenz model for El Niño

Garay, Barnabás M.; Indig, Balázs

doi:10.1016/j.chaos.2015.02.015

Cited by 20 publications

(8 citation statements)

References 25 publications

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“…System (228) is comparable to the Lorenz system and it was shown by Vallis [50,51] that (228) with the parameters B = 102 and C = 3 is chaotic. In paper [99] the authors studied the system (228) with the same parameters and by using the computer- Next, we take into account the equations…”

Section: Coupling Of the Advection Equation With Vallis Modelmentioning

confidence: 99%

Dynamics with Chaos and Fractals

Alejaily

Fen

Akhmet³

2020

Nonlinear Systems and Complexity

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, 98 pages In this thesis, we study how to construct and analyze dynamics for chaos and fractals. After the introductory chapter, we discuss in the second chapter the chaotic behavior of hydrosphere parameters and their influence on global weather and climate. For this purpose, we investigate the nature and source of unpredictability in the dynamics of sea surface temperature. The impact of sea surface temperature variability on the global climate is clear during some global climate patterns like the El Niño-Southern Oscillation. The interactions between these types of global climate patterns may transmit chaos. We discuss the unpredictability as a global phenomenon through extension of chaos horizontally and vertically by using theoretical as well as numerical analyses. In the third chapter, we introduce a technique concerning the construction of dynamics for fractals. Deterministic fractals like Julia sets are crucial for understanding the fractal phenomenon. These structures are deterministically arising from simple dynamics of iteration of analytic functions. On the basis of the dynamics, we develop a scheme to map fractals through iterations. This allows to involve fractals as states of dynamical systems as well as to introduce dynamics in fractals through differential and discrete equations. Creation of effective frameworks v for applications of fractals and assisting to explore the relationship between fractals and chaos by the involvement of dynamics in fractals are important aspects in this direction.

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Section: Coupling Of the Advection Equation With Vallis Modelmentioning

confidence: 99%

Dynamics with Chaos and Fractals

Alejaily

Fen

Akhmet³

2020

Nonlinear Systems and Complexity

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“…α 1 has been plotted in fig. (6). Table (4) shows values of LLE for some values of fractional order α 1 .…”

Section: Incommensurate Vallis Systemmentioning

confidence: 99%

“…Over the years, integer order Vallis system has been analyzed in various articles [6,7,8]. The chaos and periodicity of Vallis model has been investigated in depth for the integer order model over B − c parameter space [9].…”

Section: Introductionmentioning

confidence: 99%

Chaotic dynamics of fractional Vallis system for El-Niño

Deshpande

Daftardar-Gejji

2019

FCAA

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Vallis proposed a simple model for El-Niño weather phenomenon (referred as Vallis system) by adding an additional parameter p to the Lorenz system. He showed that the chaotic behavior of the Vallis system is related to the El-Niño effect. In the present article we study fractional version of Vallis system in depth. We investigate bifurcations and chaos present in the fractional Vallis system along with the effect of variation of system parameter p. It is observed that the range of values of parameter p for which the Vallis system is chaotic, reduces with the reduction of the fractional order.Further we analyze the incommensurate fractional Vallis system and find the critical value below which the system loses chaos. We also synchronize Vallis system with Bhalekar-Gejji system.

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“…The bifurcation diagram shows the change in the topology of the system as the bifurcation parameter is varied [25]. It is especially useful for studying nonlinear oscillators as it shows when the system's behavior is chaotic [26].…”

Section: F Hajdumentioning

confidence: 99%

Numerical examination of nonlinear oscillators

Hajdú

2018

Pollack Periodica

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The numerical examination of nonlinear oscillators is presented in this paper. First some methods of nonlinear system modeling are described then the numerical creation of phaseplane, bifurcation diagrams and Poincaré sections are expounded in detail. The next part of the paper is the numerical examination of nonlinear oscillators, like the Duffing-Holmes oscillator and a mechatronic semi-active suspension system. The paper concludes with further development tasks.

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Chaos in Vallis’ asymmetric Lorenz model for El Niño

Cited by 20 publications

References 25 publications

Dynamics with Chaos and Fractals

Dynamics with Chaos and Fractals

Chaotic dynamics of fractional Vallis system for El-Niño

Numerical examination of nonlinear oscillators

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