The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems (Q1081931)
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scientific article; zbMATH DE number 3971827
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems |
scientific article; zbMATH DE number 3971827 |
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The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems (English)
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1986
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Through extensive numerical simulation, we have characterized the transition to chaos of the solutions to the Kuramoto-Sivashinsky equation. The attracting solution manifolds undergo a complex bifurcation sequence including multimodal fixed points, invariant tori, traveling wave trains, and homoclinic orbits. We relate this behavior to earlier work where the Kuramoto-Sivashinsky equation was shown to behave as a finite dimensional dynamical system of ordinary differential equations.
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Kuramoto-Sivashinsky equation
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finite dimensional dynamical system of ordinary differential equations
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