Transition to spatio-temporal chaos in the regularized long-wave equation
Regularization of planar Filippov Systems near a codimension one singularity
Regularized families and evolution equations: qualitative properties
Full text | |
Author(s): |
Podvigina, O.
[1]
;
Zheligovsky, V.
[1]
;
Rempel, E. L.
[2, 3, 4]
;
Chian, A. C. -L.
[2, 3, 5, 4]
;
Chertovskih, R.
[4]
;
Munoz, P. R.
[4, 6]
Total Authors: 6
|
Affiliation: | [1] Russian Acad Sci, Inst Earthquake Predict Theory & Math Geophys, Moscow 117997 - Russia
[2] Natl Inst Space Res INPE, BR-12227010 Sao Jose Dos Campos, SP - Brazil
[3] WISER, BR-12227010 Sao Jose Dos Campos, SP - Brazil
[4] Inst Aeronaut Technol IEFM ITA, BR-12228900 Sao Jose Dos Campos, SP - Brazil
[5] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005 - Australia
[6] Univ La Serena, Dept Fis & Astron, La Serena - Chile
Total Affiliations: 6
|
Document type: | Journal article |
Source: | Physical Review E; v. 92, n. 3 SEP 14 2015. |
Web of Science Citations: | 0 |
Abstract | |
We perform a two-parameter bifurcation study of the driven-damped regularized long-wave equation by varying the amplitude and phase of the driver. Increasing the amplitude of the driver brings the system to the regime of spatiotemporal chaos (STC), a chaotic state with a large number of degrees of freedom. Several global bifurcations are found, including codimension-two bifurcations and homoclinic bifurcations involving three-tori and the manifolds of steady waves, leading to the formation of chaotic saddles in the phase space. We identify four distinct routes to STC; they depend on the phase of the driver and involve boundary and interior crises, intermittency, the Ruelle-Takens scenario, the Feigenbaum cascade, an embedded saddle-node, homoclinic, and other bifurcations. This study elucidates some of the recently reported dynamical phenomena. (AU) | |
FAPESP's process: | 11/10466-1 - Turbulence and coherent structures in astrophysical plasmas |
Grantee: | Pablo Rubén Muñoz Gutberlet |
Support Opportunities: | Scholarships in Brazil - Post-Doctorate |
FAPESP's process: | 13/22314-7 - Magnetic fields and dynamos in space and astrophysical plasmas II |
Grantee: | Erico Luiz Rempel |
Support Opportunities: | Regular Research Grants |
FAPESP's process: | 12/22243-0 - Magnetic dynamos driven by turbulent flows |
Grantee: | Erico Luiz Rempel |
Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
FAPESP's process: | 12/22285-4 - Transition to spatio-temporal chaos in the regularized long-wave equation |
Grantee: | Erico Luiz Rempel |
Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
FAPESP's process: | 13/01242-8 - Generation of large-scale magnetic field by Rayleigh-Bénard convection |
Grantee: | Roman Chertovskikh |
Support Opportunities: | Scholarships in Brazil - Post-Doctorate |