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Stabilization of traveling waves on dissipative system near subcritical bifurcation through a combination of global and local feedback

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Abstract

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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Data Availability Statement

The datasets generated during and/or analyzed in the current study are available from the corresponding author on reasonable request. This manuscript has associated data in a data repository. [Authors’ comment: All data include in this manuscript are available upon request by contacting with the corresponding author.].

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Acknowledgements

The authors would like to acknowledge the anonymous referees and the editor for their helpful comments, recommendations and discussions.

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Authors and Affiliations

  1. 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

    N. C. Tsague Mezamo, V. Bami Nana, F. Waffo Tchuimmo & Laurent Nana

Authors
  1. N. C. Tsague Mezamo
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  2. V. Bami Nana
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  3. F. Waffo Tchuimmo
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  4. Laurent Nana
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Contributions

L. N. conceived the idea of the present work. N. C. T. M. and F. W. T. have performed the analytical and numerical computations. V. B. N. refined the numerical computations. N. C. T. M., F. W. T. and L. N. conducted the interpretation of the results. N. C. T. M. and L. N. wrote an initial draft. F. W. T. and L. N. finalized the project.

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Correspondence to Laurent Nana.

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Mezamo, N.C.T., Nana, V.B., Tchuimmo, F.W. et al. Stabilization of traveling waves on dissipative system near subcritical bifurcation through a combination of global and local feedback. Eur. Phys. J. Plus 137, 1139 (2022). https://doi.org/10.1140/epjp/s13360-022-03352-9

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