title: Two-parameter bifurcation study of the regularized long-wave equation.
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.
authors.affiliation: Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, 84/32 Profsoyuznaya Street, 117997 Moscow, Russian Federation.
authors.forename: O
authors.initials: O
authors.lastname: Podvigina
authors.affiliation: Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, 84/32 Profsoyuznaya Street, 117997 Moscow, Russian Federation.
authors.forename: V
authors.initials: V
authors.lastname: Zheligovsky
authors.affiliation: Institute of Aeronautical Technology (IEFM/ITA), São José dos Campos, São Paulo 12228-900, Brazil.|National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, São José dos Campos, São Paulo 12227-010, Brazil.
authors.forename: E L
authors.initials: EL
authors.lastname: Rempel
authors.affiliation: Institute of Aeronautical Technology (IEFM/ITA), São José dos Campos, São Paulo 12228-900, Brazil.|National Institute for Space Research (INPE) and World Institute for Space Environment Research (WISER), P.O. Box 515, São José dos Campos, São Paulo 12227-010, Brazil.|School of Mathematical Sciences, University of Adelaide, Adelaide, SA 5005, Australia.
authors.forename: A C-L
authors.initials: AC
authors.lastname: Chian
authors.affiliation: Institute of Aeronautical Technology (IEFM/ITA), São José dos Campos, São Paulo 12228-900, Brazil.
authors.forename: R
authors.initials: R
authors.lastname: Chertovskih
authors.affiliation: Institute of Aeronautical Technology (IEFM/ITA), São José dos Campos, São Paulo 12228-900, Brazil.|Departamento de Física y Astronomía, Universidad de La Serena, Avenue Cisternas 1200, La Serena, Chile.
authors.forename: P R
authors.initials: PR
authors.lastname: Muñoz