Nonlinear Dynamical Processes Described by the Traveling Wave Reduction of the Generalized Kuramoto–Sivashinsky Equation
https://doi.org/10.56304/S2304487X20020091
Abstract
The generalized Kuramoto–Sivashinsky equation is used to describe a lot of nonlinear physical processes. In this work, dynamical regimes described by the traveling wave reduction of the generalized Kuramoto–Sivashinsky equation are examined. The main goal of this work is to study how the dispersive term suppresses chaotic regimes in the system. The traveling wave reduction of the Kuramoto–Sivashinsky equation is written in the normal form. The divergence of the vector field this system has been calculated. The parameters for which the studied system is dissipative have been determined. The bifurcation diagram is plotted for three different nonlinearity degrees of the generalized Kuramoto–Sivashinsky equation. The dispersion term coefficient is chosen as the bifurcation parameter. The largest Lyapunov exponent is plotted as a function of the dispersion parameter for the three studied cases. The Benettin algorithm is employed to compute largest Lyapunov exponents. It has been found that a chaotic regime is observed in the system at some values of the dispersion parameter. Routes to chaos are described. Phase portraits for some of the dynamical regimes are presented.
About the Authors
S. F. Lavrova
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
Moscow
N. A. Kudryashov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
Moscow
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Review
For citations:
Lavrova S.F., Kudryashov N.A. Nonlinear Dynamical Processes Described by the Traveling Wave Reduction of the Generalized Kuramoto–Sivashinsky Equation. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2020;9(2):129-138. (In Russ.) https://doi.org/10.56304/S2304487X20020091
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