2002/05/02 by Diego Pazó, V. Pérez‐Muñuzuri, Vicente Pérez-Muñuzuri +1
Computer Science · Health Professions · Physics and Astronomy · #Chaos control and synchronization #Food Security and Health in Diverse Populations #Information and Cyber Security #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #nlin.CD #nlin.PS
paper · pdf · doi:10.1063/1.1586511
25 pages (17 figures included), submitted to Physica D
arxiv created 2002/05/02 · openalex publication_date 2006/03/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Traveling fronts are shown to occur in an array of nearest-neighbor coupled symmetric bistable units. When the local dynamics is given by the Lorenz equations we observe the route: standing-->oscillating-->traveling front, as the coupling is increased. A key step in this route is a gluing bifurcation of two cycles in cylindrical coordinates. When this is mediated by a saddle with real leading eigenvalues, the asymptotic behavior of the front velocity is found straightforwardly. If the saddle is focus-type instead, the front's dynamics may become quite complex, displaying several oscillating and propagating regimes and including (Shil'nikov-type) chaotic front propagation. These results stand as well for other nearest-neighbor coupling schemes and local dynamics.