Dynamical Analysis of the Lorenz-84 Atmospheric Circulation Model

Hu, Wang; Yu, Yongguang; Wen, Guoguang

doi:10.1155/2014/296279

Cited by 11 publications

(3 citation statements)

References 33 publications

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“…5(a)] reveals a very rich collection of bifurcations. [25][26][27][28] The co-existence of at least two attractors is shown by computing the bifurcation diagram by increasing (black) and decreasing (red) the parameter a. For instance, when a is increased, a period-2 limit cycle [whose upper segment is shown in the blowup of Fig.…”

Section: B the Weakly Dissipative Lorenz 84 Systemmentioning

confidence: 99%

Synchronizability of nonidentical weakly dissipative systems

Sendiña‐Nadal

Letellier

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Synchronization is a very generic process commonly observed in a large variety of dynamical systems which, however, has been rarely addressed in systems with low dissipation. Using the Rössler, the Lorenz 84, and the Sprott A systems as paradigmatic examples of strongly, weakly, and non-dissipative chaotic systems, respectively, we show that a parameter or frequency mismatch between two coupled such systems does not affect the synchronizability and the underlying structure of the joint attractor in the same way. By computing the Shannon entropy associated with the corresponding recurrence plots, we were able to characterize how two coupled nonidentical chaotic oscillators organize their dynamics in different dissipation regimes. While for strongly dissipative systems, the resulting dynamics exhibits a Shannon entropy value compatible with the one having an average parameter mismatch, for weak dissipation synchronization dynamics corresponds to a more complex behavior with higher values of the Shannon entropy. In comparison, conservative dynamics leads to a less rich picture, providing either similar chaotic dynamics or oversimplified periodic ones.

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Section: B the Weakly Dissipative Lorenz 84 Systemmentioning

confidence: 99%

Synchronizability of nonidentical weakly dissipative systems

Sendiña‐Nadal

Letellier

2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Soon afterward, Kuznetsov et al discussed the fold-flip bifurcation in the Lorenz-84 model [14]. The literature [15] discussed the bifurcation and chaotic behavior of the Lorenz-84 model without seasonal forcing. Especially, a computer-assisted proof of the chaoticity of the model is also presented by a topological horseshoe theory.…”

Section: Introductionmentioning

confidence: 99%

Attractor and bifurcation of forced Lorenz-84 system

Liu

Wei

et al. 2019

Int. J. Geom. Methods Mod. Phys.

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In this paper, global dynamics of forced Lorenz-84 system are discussed, and some new results are presented. First of all, the periodic attractor is analyzed for the almost periodic Lorenz-84 system with almost periodically forcing, including the existence and the boundedness of those almost periodic solutions, and the bifurcation phenomenon in the driven system. Then, the random attractor set and the bifurcation phenomenon for the driven Lorenz-84 system with stochastic forcing are studied, including the globally exponentially attractive set, positive invariant set, random attractor and stochastic bifurcation behavior. Last but not least, some numerical simulations are also presented for verifying obtained theoretical results.

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“…In terms of dynamical systems based on the spring-block model, the presence of oscillations and self-oscillations can be explained by the Hopf bifurcation mechanism (Kengne et al, 2014;Meng and Huo, 2014;Wang et al, 2014). Some nonlinear dynamical systems show self-sustained oscillation (SSO) motion (Strogatz, 1994), one of them being relative to the earthquake physics mechanism (Scholz, 1998).…”

Section: Introductionmentioning

confidence: 99%

An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces

Castellanos-Rodríguez¹,

Campos-Cantón²,

Barboza-Gudiño³

et al. 2017

Nonlin. Processes Geophys.

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The complex oscillatory behavior of a springblock model is analyzed via the Hopf bifurcation mechanism. The mathematical spring-block model includes Dieterich-Ruina's friction law and Stribeck's effect. The existence of self-sustained oscillations in the transition zone -where slow earthquakes are generated within the frictionally unstable region -is determined. An upper limit for this region is proposed as a function of seismic parameters and frictional coefficients which are concerned with presence of fluids in the system. The importance of the characteristic length scale L, the implications of fluids, and the effects of external perturbations in the complex dynamic oscillatory behavior, as well as in the stationary solution, are take into consideration.

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Dynamical Analysis of the Lorenz-84 Atmospheric Circulation Model

Cited by 11 publications

References 33 publications

Synchronizability of nonidentical weakly dissipative systems

Synchronizability of nonidentical weakly dissipative systems

Attractor and bifurcation of forced Lorenz-84 system

An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces

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