Two-parameter bifurcation study of the regularized long-wave equation

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Podvigina, O (Author) Other; Zheligovsky, V (Author) Other; Rempel, EL (Author) Other; Chian, ACL (Author) Other; Chertovskih, R (Author) Other; Muñoz, PR (Author) Other

Journal

Title: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Vol. 92

ISSN: 1539-3755

Publisher: American Physical Society

Indexing

Scopus - 1 Citation

Other information

Authenticus ID: P-00N-GGC

DOI: 10.1103/physreve.92.032906

Abstract (EN): 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. © 2015 American Physical Society.

Language: English

Type (Professor's evaluation): Scientific