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Dynamics of plane waves on two-dimensional isotropic and anisotropic dissipative systems near subcritical bifurcation

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Abstract

In this work, stability analysis of plane wave solutions of the cubic-quintic complex Ginzburg–Landau equation for isotropic and anisotropic systems is carried out. In this regard, we perform extensive numerical simulations based on a two-dimensional spatial Fourier discretization and an explicit scheme for temporal differentiation to find the domain of existence of the space-time dynamical behavior of the two-dimensional complex Ginzburg–Landau equation with cubic and quintic nonlinearities. One of the nonlinearity parameters is fixed and the others are varied one by one to determine the regimes in which plane wave solutions exist as stable/instable structures. Moreover, the stability criterion which has been plotted with the state diagram and the different dynamic structures obtained in space parameters has been established. Energy function was also used to characterize spatiotemporal dynamics observed in our system. By performing long simulations for the different parameters of the equation, we found the existence of stable (plane wave, localized defect), intermittent (intermittency state), and unstable (bichaos, phase turbulence, and defect turbulence) structures.

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The datasets generated and analyzed in the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their useful and valuable comments and suggestions.

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  1. Pure Physics Laboratory, Group of Nonlinear phenomena in Complex Systems, Department of Physics, Faculty of Sciences, University of Douala, P.O. Box 24157, Douala, Cameroon

    Jimmy Franklin Beltchui Nzoukeu, Thibaut Patient Nana Leufak & Laurent Nana

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Beltchui Nzoukeu, J.F., Nana Leufak, T.P. & Nana, L. Dynamics of plane waves on two-dimensional isotropic and anisotropic dissipative systems near subcritical bifurcation. Nonlinear Dyn 111, 17427–17438 (2023). https://doi.org/10.1007/s11071-023-08753-8

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