https://repository.biust.ac.bw/handle/123456789/137 This collection contains electronic copies of books, chapters and sections produced by staff and students of Faculty of Sciences, BIUST. 2026-04-15T00:05:40Z https://repository.biust.ac.bw/handle/123456789/320 Nonlinear dynamical regimes and control of turbulence through the complex Ginzburg-Landau equation Tafo, Joël Bruno Gonpe; Nana, Laurent; Tabi, Conrad Bertrand; Kofané, Timoléon Crépin The dynamical behavior of pulse and traveling hole in a one-dimensional system depending on the boundary conditions, obeying the complex Ginzburg-Landau (CGL) equation, is studied numerically using parameters near a subcritical bifurca- tion. In a spatially extended system, the criterion of Benjamin-Feir-Newell (BFN) instability near the weakly inverted bifurcation is established, and many types of regimes such as laminar regime, spatiotemporal regime, defect turbulence regimes, and so on are observed. In finite system by using the homogeneous boundary conditions, two types of regimes are detected mainly the convective and the absolute instability. The convectively unstable regime appears below the threshold of the parameter control, and beyond, the absolute regime is observed. Controlling such regimes remains a great challenge; many methods such as the nonlinear diffusion parameter control are used. The unstable traveling hole in the one- dimensional cubic-quintic CGL equation may be effectively stabilized in the chaotic regime. In order to stabilize defect turbulence regimes, we use the global time-delay auto-synchronization control; we also use another method of control which consists in modifying the nonlinear diffusion term. Finally, we control the unstable regimes by adding the nonlinear gradient term to the system. We then notice that the chaotic system becomes stable under strong nonlinearity. 2020-03-11T00:00:00Z