Amplitude-Phase Synchronization at the Onset of Permanent Spatiotemporal Chaos

Chian, Abraham C.‐L.; Miranda, Rodrigo A.; Rempel, Erico L.; Saiki, Yoshitaka; Yamada, Michio

doi:10.1103/physrevlett.104.254102

Cited by 32 publications

(37 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The laminar structure of Fig. 2(c), corresponding to a spatially regular and temporally chaotic attractor, has one positive Lyapunov exponent and a Kaplan-Yorke dimension of ∼ 22 [10].…”

Section: (A)mentioning

confidence: 99%

“…The driven-damped regularized long-wave equation in dimensionless units is given by [8,10] ∂ t u + c∂ x u + f u∂ x u + a∂ txx u = −νu − sin(κx − Ωt) (1) where is the driver amplitude, c = 1, f = −6, a = −0.28711, ν = 0.1, κ = 1 and Ω = 0.65. We impose periodic boundary conditions u(x, t) = u(x + 2π, t) and solve Eq.…”

Section: The Modelmentioning

confidence: 99%

“…2. We characterize the degree of spatiotemporal disorder of each structure by computing the Lyapunov spectrum {λ j } and the Kaplan-Yorke dimension [10,13], defined as…”

Section: (A)mentioning

confidence: 99%

“…The RLWE is an improved model of nonlinear smallamplitude long-waves in fluids, first derived by Peregrine [6], then by Benjamin et al [7] to remove some mathematical problems associated with the Kortweg-de Vries * abraham.chian@gmail.com equation, such as the existence and stability of solutions and other problems related to the dispersion term. Dynamical systems description of the transition from temporally to spatiotemporally chaotic attractors, based on the RLWE, provides a simple model to acquire in-depth insights on the laminar-turbulence transition [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Edge of chaos and genesis of turbulence

2013

Self Cite

View full text Add to dashboard Cite

The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable travelling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space.

show abstract

“…The laminar structure of Fig. 2(c), corresponding to a spatially regular and temporally chaotic attractor, has one positive Lyapunov exponent and a Kaplan-Yorke dimension of ∼ 22 [10].…”

Section: (A)mentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

“…2. We characterize the degree of spatiotemporal disorder of each structure by computing the Lyapunov spectrum {λ j } and the Kaplan-Yorke dimension [10,13], defined as…”

Section: (A)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Edge of chaos and genesis of turbulence

2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…Another technique to investigate phase information, used thus far in the context of the solar wind community, is the socalled phase coherence index (PCI, see Hada et al 2003;Koga et al 2007;Chian et al 2008Chian et al , 2010. The PCI employs two surrogate data sets: one in which the phase information in an image or signal is randomized and another in which the phase information is perfectly correlated.…”

Section: Introductionmentioning

confidence: 99%

The Phase Coherence of Interstellar Density Fluctuations

Burkhart

Lazarían

2016

ApJ

View full text Add to dashboard Cite

Studies of MHD turbulence often investigate the Fourier power spectrum to provide information on the nature of the turbulence cascade. However, the Fourier power spectrum only contains the Fourier amplitudes and rejects all information regarding the Fourier phases. Here, we investigate the utility of two statistical diagnostics for recovering information on Fourier phases in ISM column density maps: the averaged amplitudes of the bispectrum and the phase coherence index (PCI), a new phase technique for the ISM. We create three-dimensional density and two-dimensional column density maps using a set of simulations of isothermal ideal MHD turbulence with a wide range of sonic and Alfvénic Mach numbers. We find that the bispectrum averaged along different angles with respect to either the k 1 or k 2 axis is primarily sensitive to the sonic Mach number while averaging the bispectral amplitudes over different annuli is sensitive to both the sonic and Alfvénic Mach numbers. The PCI of density suggests that the most correlated phases occur in supersonic sub-Alfvénic turbulence and near the shock scale. This suggests that nonlinear interactions with correlated phases are strongest in shock-dominated regions, in agreement with findings from the solar wind. Our results suggest that the phase information contained in the bispectrum and PCI can be used to find the turbulence parameters in column density maps.

show abstract

Nonlinear dynamics in space plasma turbulence: temporal stochastic chaos

Chian

Borotto

Hada

et al. 2022

Rev. Mod. Plasma Phys.

View full text Add to dashboard Cite

Intermittent turbulence is key for understanding the stochastic nonlinear dynamics of space, astrophysical, and laboratory plasmas. We review the theory of deterministic and stochastic temporal chaos in plasmas and discuss its link to intermittent turbulence observed in space plasmas. First, we discuss the theory of chaos, intermittency, and complexity for nonlinear Alfvén waves, and parametric decay and modulational wave–wave interactions, in the absence/presence of noise. The transition from order to chaos is studied using the bifurcation diagram. The following two types of deterministic intermittent chaos in plasmas are considered: type-I Pomeau–Manneville intermittency and crisis-induced intermittency. The role of structures known as chaotic saddles in deterministic and stochastic chaos in plasmas is investigated. Alfvén complexity associated with noise-induced intermittency, in the presence of multistability, is studied. Next, we present evidence of magnetic reconnection and intermittent magnetic turbulence in coronal mass ejections in the solar corona and solar wind via remote and in situ observations. The signatures of turbulent magnetic reconnection, i.e., bifurcated current sheet, reconnecting jet, parallel/anti-parallel Alfvénic waves, and spiky dynamical pressure pulse, as well as fully developed turbulence, are detected at the leading edge of an interplanetary coronal mass ejection and the interface region of two merging interplanetary magnetic flux ropes. Methods for quantifying the degree of coherence, amplitude–phase synchronization, and multifractality of nonlinear multiscale fluctuations are discussed. The stochastic chaotic nature of Alfvénic intermittent structures driven by magnetic reconnection is determined by a complexity–entropy analysis. Finally, we discuss the relation of nonlinear dynamics and intermittent turbulence in space plasmas to similar phenomena observed in astrophysical and laboratory plasmas, e.g., coronal mass ejections and flares in the stellar-exoplanetary environment and Galactic Center, as well as chaos, magnetic reconnection, and intermittent turbulence in laser-plasma and nuclear fusion experiments.

show abstract

Amplitude-Phase Synchronization at the Onset of Permanent Spatiotemporal Chaos

Cited by 32 publications

References 26 publications

Edge of chaos and genesis of turbulence

Edge of chaos and genesis of turbulence

The Phase Coherence of Interstellar Density Fluctuations

Nonlinear dynamics in space plasma turbulence: temporal stochastic chaos

Contact Info

Product

Resources

About