Stabilization of traveling waves on dissipative system near subcritical bifurcation through a combination of global and local feedback
Pure Physics Laboratory, Group of Nonlinear Physics and Complex Systems, Department of Physics, Faculty of science, University of Douala, P.O. Box 24157, Douala, Cameroon
Accepted: 1 October 2022
Published online: 15 October 2022
In this study, we develop bifurcation analysis of the traveling wave solutions of a system governed by sub-critical complex Ginzburg-Landau equation with local and global time-delay feedback. In this approach, taking into account the time-delay feedback we show how bistability, multistability and snaking behavior of traveling waves emerge in the system. We analyze analytically and numerically the stability of traveling waves depending on the feedback parameters. We investigate the system in the regime of spatiotemporal turbulence and study how a combination of global and local time-delay feedback can be used to suppress turbulence by inducing uniform oscillations. Direct numerical simulations show that a mixed local and global feedback can be efficient and also able to create stable patterns in the system. The dynamic of traveling wave in the system is studied numerically through a construction of states diagrams, a computation of the energy function and the Lyapunov exponent.
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