Two-parameter bifurcation study of the regularized long-wave equation
Date
2015
Authors
Podvigina, O.
Zheligovsky, V.
Rempel, E.
Chian, A.
Chertovskih, R.
Muñoz, P.
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Journal article
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Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 2015; 92(3):032906-1-032906-14
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O. Podvigina, V. Zheligovsky, E.L. Rempel, A.C.-L. Chian, R. Chertovskih, and P.R. Muñoz
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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.
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© 2015 American Physical Society