Complex dynamics in the 1:3 spatial resonance (Q1587728)
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scientific article; zbMATH DE number 1538308
| Language | Label | Description | Also known as |
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| English | Complex dynamics in the 1:3 spatial resonance |
scientific article; zbMATH DE number 1538308 |
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Complex dynamics in the 1:3 spatial resonance (English)
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5 February 2001
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The authors consider the interaction between two steady-state bifurcations with spacial wave numbers in the ratio \(1:3\). They assume periodic boundary conditions. The resulting \(O(2)\) equivariant normal form, truncated at the third order, exhibits a number of global bifurcations that may result in complex dynamics. A careful numerical simulation and analysis of appropriate return maps help to elucidate this behavior. The results generalize to other \(1:n\) resonances.
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spacial resonance
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local and global bifurcations
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complex dynamics
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